यदि (7-4x>19) है तो (x) का सही हल कौन सा है?
If (7-4x>19), which solution for (x) is correct?
#linear-inequality
#negative-division
#sign-reversal
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A (x<-3)
B (x>3)
C (x<3)
D (x>-3)
Explanation opens after your attempt
Step 1
Concept
From (7-4x>19), we get (-4x>12), so (x<-3). The inequality sign reverses when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. (x<-3). From (7-4x>19), we get (-4x>12), so (x<-3). The inequality sign reverses when dividing by a negative number.
Step 3
Exam Tip
(7-4x>19) से (-4x>12) और (x<-3) मिलता है। ऋणात्मक संख्या से भाग देते समय असमता का चिन्ह पलटता है।
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यदि \(x\in\mathbb{R}\) और \(-7<2x+5\leq 13\) है तो (x) का सही हल कौन सा है?
If \(x\in\mathbb{R}\) and \(-7<2x+5\leq 13\), which solution for (x) is correct?
#compound-inequality
#real-solution
#interval
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A \(-6<x\leq 4\)
B \(-6\leq x<4\)
C \(-1<x\leq 9\)
D \(-1\leq x<9\)
Explanation opens after your attempt
Correct Answer
A. \(-6<x\leq 4\)
Step 1
Concept
Subtracting (5) gives \(-12<2x\leq 8\), then \(-6<x\leq 4\). Apply the same operation to every part of a compound inequality.
Step 2
Why this answer is correct
The correct answer is A. \(-6<x\leq 4\). Subtracting (5) gives \(-12<2x\leq 8\), then \(-6<x\leq 4\). Apply the same operation to every part of a compound inequality.
Step 3
Exam Tip
(5) घटाने पर \(-12<2x\leq 8\) और फिर \(-6<x\leq 4\) मिलता है। संयुक्त असमता में हर भाग पर समान क्रिया करें।
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यदि \(x\in\mathbb{R}\) और \(\frac{5-2x}{3}\geq \frac{x+1}{6}\) है तो (x) का सही हल कौन सा है?
If \(x\in\mathbb{R}\) and \(\frac{5-2x}{3}\geq \frac{x+1}{6}\), which solution for (x) is correct?
#fractional-inequality
#lcm
#error-check
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A \(x\leq 3\)
B \(x\geq 3\)
C \(x\leq -3\)
D \(x\geq -3\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 3\)
Step 1
Concept
Multiplying by (6) gives \(10-4x\geq x+1\), so \(9\geq 5x\). Therefore \(x\leq \frac{9}{5}\), so none of the listed options should be correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 3\). Multiplying by (6) gives \(10-4x\geq x+1\), so \(9\geq 5x\). Therefore \(x\leq \frac{9}{5}\), so none of the listed options should be correct.
Step 3
Exam Tip
(6) से गुणा करने पर \(10-4x\geq x+1\) और \(9\geq 5x\) मिलता है। इसलिए \(x\leq \frac{9}{5}\) होता है, अतः सही विकल्पों में कोई नहीं होना चाहिए।
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असमता (5(2x-3)\leq 3x+20) का हल कौन सा है?
What is the solution of (5(2x-3)\leq 3x+20)?
#bracket-expansion
#linear-inequality
#solution
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A \(x\leq 5\)
B \(x\geq 5\)
C \(x\leq -5\)
D \(x\geq -5\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 5\)
Step 1
Concept
Simplifying gives \(10x-15\leq 3x+20\), so \(7x\leq 35\). After opening brackets, place like terms correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 5\). Simplifying gives \(10x-15\leq 3x+20\), so \(7x\leq 35\). After opening brackets, place like terms correctly.
Step 3
Exam Tip
सरलीकरण से \(10x-15\leq 3x+20\) और \(7x\leq 35\) मिलता है। कोष्ठक खोलने के बाद समान पदों को सही ओर रखें।
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असमता \(\frac{3-x}{-4}<2\) का हल कौन सा है?
What is the solution of \(\frac{3-x}{-4}<2\)?
#negative-denominator
#sign-reversal
#fractional-inequality
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A (x<11)
B (x>11)
C (x<-5)
D (x>-5)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (-4) reverses the sign and gives (3-x>-8). This gives (-x>-11), so (x<11).
Step 2
Why this answer is correct
The correct answer is A. (x<11). Multiplying by (-4) reverses the sign and gives (3-x>-8). This gives (-x>-11), so (x<11).
Step 3
Exam Tip
(-4) से गुणा करने पर चिन्ह पलटकर (3-x>-8) मिलता है। इससे (-x>-11) और (x<11) प्राप्त होता है।
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यदि \(x\in\mathbb{Z}\) और (4x+9<1) है तो सबसे बड़ा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and (4x+9<1), what is the greatest possible (x)?
#integer-solution
#greatest-value
#strict-inequality
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A (0)
B (-1)
C (-2)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (4x<-8), so (x<-2). The greatest integer less than (-2) is (-3).
Step 2
Why this answer is correct
The correct answer is C. (-2). The inequality gives (4x<-8), so (x<-2). The greatest integer less than (-2) is (-3).
Step 3
Exam Tip
असमता से (4x<-8) इसलिए (x<-2) मिलता है। सबसे बड़ा पूर्णांक हल (-3) नहीं बल्कि (-3) से पहले जांचें और सही मान (-3) होगा।
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किसी संख्या के (2) गुने में से (5) घटाने पर परिणाम उसी संख्या से (3) अधिक से कम नहीं है। सही असमता और हल कौन सा है?
Twice a number decreased by (5) is not less than (3) more than the number. Which inequality and solution are correct?
#word-problem
#inequality-formation
#solution
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A \(2x-5\geq x+3,\ x\geq 8\)
B (2x-5>x+3,\ x>8)
C \(2x-5\leq x+3,\ x\leq 8\)
D (2x-5<x+3,\ x<8)
Explanation opens after your attempt
Correct Answer
A. \(2x-5\geq x+3,\ x\geq 8\)
Step 1
Concept
Not less than means \(\geq\). From \(2x-5\geq x+3\), we get \(x\geq 8\).
Step 2
Why this answer is correct
The correct answer is A. \(2x-5\geq x+3,\ x\geq 8\). Not less than means \(\geq\). From \(2x-5\geq x+3\), we get \(x\geq 8\).
Step 3
Exam Tip
कम नहीं है का अर्थ \(\geq\) होता है। \(2x-5\geq x+3\) से \(x\geq 8\) मिलता है।
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अंतराल (\(-\infty,-6]\) को असमता के रूप में कैसे लिखेंगे?
How is the interval (\(-\infty,-6]\) written as an inequality?
#interval-notation
#closed-endpoint
#inequality-form
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A (x<-6)
B \(x\leq -6\)
C (x>-6)
D \(x\geq -6\)
Explanation opens after your attempt
Correct Answer
B. \(x\leq -6\)
Step 1
Concept
The right endpoint (-6) is closed, so (-6) is included. Therefore the inequality is \(x\leq -6\).
Step 2
Why this answer is correct
The correct answer is B. \(x\leq -6\). The right endpoint (-6) is closed, so (-6) is included. Therefore the inequality is \(x\leq -6\).
Step 3
Exam Tip
दायां सिरा (-6) बंद है इसलिए (-6) शामिल होगा। अतः असमता \(x\leq -6\) है।
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यदि \(x\in\mathbb{Z}\) और \(-2\leq \frac{x-1}{3}<3\) है तो पूर्णांक हलों की संख्या कितनी है?
If \(x\in\mathbb{Z}\) and \(-2\leq \frac{x-1}{3}<3\), how many integer solutions are there?
#integer-count
#compound-fraction
#solution-set
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A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (3) gives \(-6\leq x-1<9\), so \(-5\leq x<10\). The integers from (-5) to (9) are (15) in total.
Step 2
Why this answer is correct
The correct answer is B. (15). Multiplying by (3) gives \(-6\leq x-1<9\), so \(-5\leq x<10\). The integers from (-5) to (9) are (15) in total.
Step 3
Exam Tip
(3) से गुणा करने पर \(-6\leq x-1<9\), इसलिए \(-5\leq x<10\) मिलता है। पूर्णांक (-5) से (9) तक हैं, कुल (15)।
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यदि \(-9\leq 3x-6<12\) है तो (x) का सही अंतराल कौन सा है?
If \(-9\leq 3x-6<12\), which interval for (x) is correct?
#compound-inequality
#interval
#real-solution
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A ([-1,6))
B ((-1,6])
C ([-1,6])
D ((-1,6))
Explanation opens after your attempt
Correct Answer
A. ([-1,6))
Step 1
Concept
Adding (6) gives \(-3\leq 3x<18\), then \(-1\leq x<6\). Apply the same operation to all parts of a compound inequality.
Step 2
Why this answer is correct
The correct answer is A. ([-1,6)). Adding (6) gives \(-3\leq 3x<18\), then \(-1\leq x<6\). Apply the same operation to all parts of a compound inequality.
Step 3
Exam Tip
(6) जोड़ने पर \(-3\leq 3x<18\) और फिर \(-1\leq x<6\) मिलता है। संयुक्त असमता में दोनों ओर समान क्रिया करें।
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असमता (3(x-2)<3x-8) का हल समुच्चय कौन सा है?
What is the solution set of (3(x-2)<3x-8)?
#no-solution
#empty-set
#linear-inequality
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A \(\emptyset\)
B \(\mathbb{R}\)
C (\(-\infty,-2\))
D (\(-2,\infty\))
Explanation opens after your attempt
Correct Answer
A. \(\emptyset\)
Step 1
Concept
Simplifying gives (3x-6<3x-8), that is (-6<-8), which is false. A false constant statement gives solution set \(\emptyset\).
Step 2
Why this answer is correct
The correct answer is A. \(\emptyset\). Simplifying gives (3x-6<3x-8), that is (-6<-8), which is false. A false constant statement gives solution set \(\emptyset\).
Step 3
Exam Tip
सरलीकरण से (3x-6<3x-8) यानी (-6<-8) मिलता है, जो असत्य है। असत्य स्थिर कथन आने पर हल समुच्चय \(\emptyset\) होता है।
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कौन सा विकल्प (x>2) और \(x\leq 9\) का संयुक्त हल है?
Which option is the combined solution of (x>2) and \(x\leq 9\)?
#intersection
#compound-solution
#interval
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A ([2,9))
B ((2,9])
C ([2,9])
D ((2,9))
Explanation opens after your attempt
Correct Answer
B. ((2,9])
Step 1
Concept
Taking both conditions together gives \(2<x\leq 9\). Use an open endpoint for a strict sign and a closed endpoint for equality.
Step 2
Why this answer is correct
The correct answer is B. ((2,9]). Taking both conditions together gives \(2<x\leq 9\). Use an open endpoint for a strict sign and a closed endpoint for equality.
Step 3
Exam Tip
दोनों शर्तों को साथ लेने पर \(2<x\leq 9\) मिलता है। सख्त चिन्ह पर खुला सिरा और बराबरी वाले चिन्ह पर बंद सिरा रखें।
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असमता \(\frac{2x+3}{5}\geq \frac{x-1}{2}\) का हल कौन सा है?
What is the solution of \(\frac{2x+3}{5}\geq \frac{x-1}{2}\)?
#fractional-inequality
#lcm
#linear
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A \(x\leq 11\)
B \(x\geq 11\)
C \(x\leq -11\)
D \(x\geq -11\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 11\)
Step 1
Concept
Multiplying by (10) gives \(4x+6\geq 5x-5\), so \(x\leq 11\). Removing positive denominators does not change the inequality sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 11\). Multiplying by (10) gives \(4x+6\geq 5x-5\), so \(x\leq 11\). Removing positive denominators does not change the inequality sign.
Step 3
Exam Tip
(10) से गुणा करने पर \(4x+6\geq 5x-5\) और \(x\leq 11\) मिलता है। धनात्मक हर हटाने से असमता का चिन्ह नहीं बदलता।
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किस असमता का हल \([4,\infty\)) है?
Which inequality has solution \([4,\infty\))?
#identify-inequality
#interval
#closed-endpoint
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A (2x-8>0)
B \(2x-8\geq 0\)
C \(2x+8\leq 0\)
D (2x+8<0)
Explanation opens after your attempt
Correct Answer
B. \(2x-8\geq 0\)
Step 1
Concept
From \(2x-8\geq 0\), we get \(x\geq 4\). A closed endpoint comes from an equality sign.
Step 2
Why this answer is correct
The correct answer is B. \(2x-8\geq 0\). From \(2x-8\geq 0\), we get \(x\geq 4\). A closed endpoint comes from an equality sign.
Step 3
Exam Tip
\(2x-8\geq 0\) से \(x\geq 4\) मिलता है। बंद सिरा बराबरी वाले चिन्ह से आता है।
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यदि \(x\in\mathbb{N}\) और \(5x-4\leq 21\) है तो हल समुच्चय कौन सा है?
If \(x\in\mathbb{N}\) and \(5x-4\leq 21\), what is the solution set?
#natural-numbers
#solution-set
#linear-inequality
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A ({1,2,3,4,5})
B ({0,1,2,3,4,5})
C ({1,2,3,4})
D ({2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5})
Step 1
Concept
The inequality gives \(5x\leq 25\), so \(x\leq 5\). Taking positive integers in \(\mathbb{N}\), the solutions are (1) through (5).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5}). The inequality gives \(5x\leq 25\), so \(x\leq 5\). Taking positive integers in \(\mathbb{N}\), the solutions are (1) through (5).
Step 3
Exam Tip
असमता से \(5x\leq 25\) और \(x\leq 5\) मिलता है। \(\mathbb{N}\) में धनात्मक पूर्णांक लेकर हल (1) से (5) तक हैं।
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यदि (2x+5) धनात्मक नहीं है तो (x) के लिए सही असमता कौन सी है?
If (2x+5) is not positive, which inequality for (x) is correct?
#word-translation
#non-positive
#linear-inequality
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A \(x>-\frac{5}{2}\)
B \(x\geq -\frac{5}{2}\)
C \(x<-\frac{5}{2}\)
D \(x\leq -\frac{5}{2}\)
Explanation opens after your attempt
Correct Answer
D. \(x\leq -\frac{5}{2}\)
Step 1
Concept
Not positive means \(2x+5\leq 0\). This gives \(x\leq -\frac{5}{2}\).
Step 2
Why this answer is correct
The correct answer is D. \(x\leq -\frac{5}{2}\). Not positive means \(2x+5\leq 0\). This gives \(x\leq -\frac{5}{2}\).
Step 3
Exam Tip
धनात्मक नहीं है का अर्थ \(2x+5\leq 0\) है। इससे \(x\leq -\frac{5}{2}\) मिलता है।
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कौन सा मान \(-4<x\leq 3\) का हल नहीं है?
Which value is not a solution of \(-4<x\leq 3\)?
#endpoint-check
#not-solution
#compound-inequality
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A (x=-3)
B (x=0)
C (x=3)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
(-4) is an open endpoint, so (x=-4) is not included. Checking boundary values is essential in such questions.
Step 2
Why this answer is correct
The correct answer is D. (x=-4). (-4) is an open endpoint, so (x=-4) is not included. Checking boundary values is essential in such questions.
Step 3
Exam Tip
(-4) खुला सिरा है इसलिए (x=-4) शामिल नहीं है। सीमा मान जांचना ऐसे प्रश्नों में जरूरी है।
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असमता (6-2(5x-1)<0) का हल कौन सा है?
What is the solution of (6-2(5x-1)<0)?
#brackets
#negative-division
#fraction-answer
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A \(x>\frac{4}{5}\)
B \(x<\frac{4}{5}\)
C \(x>-\frac{4}{5}\)
D \(x<-\frac{4}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x>\frac{4}{5}\)
Step 1
Concept
Simplifying gives (8-10x<0), so (-10x<-8). Dividing by a negative number gives \(x>\frac{4}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(x>\frac{4}{5}\). Simplifying gives (8-10x<0), so (-10x<-8). Dividing by a negative number gives \(x>\frac{4}{5}\).
Step 3
Exam Tip
सरलीकरण से (8-10x<0) और (-10x<-8) मिलता है। ऋणात्मक संख्या से भाग देने पर \(x>\frac{4}{5}\) होगा।
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एक संख्या में (8) जोड़ने पर परिणाम (3) गुना संख्या से अधिक है। यह कथन किस असमता से व्यक्त होगा?
When (8) is added to a number, the result is greater than three times the number. Which inequality represents this statement?
#word-problem
#translation
#inequality-formation
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A (x+8>3x)
B (x+8<3x)
C \(x+8\geq 3x\)
D (8x+1>3x)
Explanation opens after your attempt
Correct Answer
A. (x+8>3x)
Step 1
Concept
Let the number be (x); the result is (x+8), and it is greater than (3x). First translate the statement into the correct algebraic inequality.
Step 2
Why this answer is correct
The correct answer is A. (x+8>3x). Let the number be (x); the result is (x+8), and it is greater than (3x). First translate the statement into the correct algebraic inequality.
Step 3
Exam Tip
कथन में संख्या (x) मानकर परिणाम (x+8) होगा और वह (3x) से अधिक है। भाषा को पहले सही बीजीय असमता में बदलें।
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यदि \(x\in\mathbb{Z}\) और \(-10<2x\leq 6\) है तो कितने पूर्णांक हल हैं?
If \(x\in\mathbb{Z}\) and \(-10<2x\leq 6\), how many integer solutions are there?
#counting-integers
#compound-inequality
#solution-set
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
Dividing gives \(-5<x\leq 3\). The integer solutions are (-4,-3,-2,-1,0,1,2,3), so there are (8).
Step 2
Why this answer is correct
The correct answer is B. (8). Dividing gives \(-5<x\leq 3\). The integer solutions are (-4,-3,-2,-1,0,1,2,3), so there are (8).
Step 3
Exam Tip
भाग देने पर \(-5<x\leq 3\) मिलता है। पूर्णांक हल (-4,-3,-2,-1,0,1,2,3) हैं इसलिए कुल (8) हैं।
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कौन सा कथन \(y\geq -7\) के बराबर है?
Which statement is equivalent to \(y\geq -7\)?
#equivalent-inequality
#notation
#reverse-order
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A \(-7\geq y\)
B \(-7\leq y\)
C (y<-7)
D \(y\leq -7\)
Explanation opens after your attempt
Correct Answer
B. \(-7\leq y\)
Step 1
Concept
Writing \(y\geq -7\) in reverse order gives \(-7\leq y\). Read the direction correctly when sides are switched.
Step 2
Why this answer is correct
The correct answer is B. \(-7\leq y\). Writing \(y\geq -7\) in reverse order gives \(-7\leq y\). Read the direction correctly when sides are switched.
Step 3
Exam Tip
\(y\geq -7\) को उलटकर लिखने पर \(-7\leq y\) होता है। पक्ष बदलते समय चिन्ह की दिशा को सही पढ़ें।
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असमता \(\frac{7-x}{3}<2\) का हल कौन सा है?
What is the solution of \(\frac{7-x}{3}<2\)?
#fraction-inequality
#negative-coefficient
#solution
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A (x>1)
B (x<1)
C (x>13)
D (x<13)
Explanation opens after your attempt
Step 1
Concept
Multiplying by positive (3) gives (7-x<6), so (-x<-1). Therefore (x>1).
Step 2
Why this answer is correct
The correct answer is A. (x>1). Multiplying by positive (3) gives (7-x<6), so (-x<-1). Therefore (x>1).
Step 3
Exam Tip
धनात्मक (3) से गुणा करने पर (7-x<6) और (-x<-1) मिलता है। इसलिए (x>1) है।
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असमता \(11\leq 2x+1\) का सबसे सरल रूप कौन सा है?
What is the simplest form of \(11\leq 2x+1\)?
#reverse-order
#simplification
#linear-inequality
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A \(x\leq 5\)
B \(x\geq 5\)
C \(x\leq 6\)
D \(x\geq 6\)
Explanation opens after your attempt
Correct Answer
B. \(x\geq 5\)
Step 1
Concept
From \(11\leq 2x+1\), we get \(10\leq 2x\), hence \(5\leq x\). This means \(x\geq 5\).
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 5\). From \(11\leq 2x+1\), we get \(10\leq 2x\), hence \(5\leq x\). This means \(x\geq 5\).
Step 3
Exam Tip
\(11\leq 2x+1\) से \(10\leq 2x\) और \(5\leq x\) मिलता है। इसका अर्थ \(x\geq 5\) है।
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यदि \(x\in\mathbb{R}\) और \(2\leq \frac{x+1}{3}<5\) है तो (x) का अंतराल कौन सा है?
If \(x\in\mathbb{R}\) and \(2\leq \frac{x+1}{3}<5\), which interval is for (x)?
#compound-fraction
#interval
#real-solution
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A ([5,14))
B ((5,14])
C ([6,15))
D ((6,15])
Explanation opens after your attempt
Correct Answer
A. ([5,14))
Step 1
Concept
Multiplying by (3) gives \(6\leq x+1<15\), hence \(5\leq x<14\). Removing a positive denominator does not change the signs.
Step 2
Why this answer is correct
The correct answer is A. ([5,14)). Multiplying by (3) gives \(6\leq x+1<15\), hence \(5\leq x<14\). Removing a positive denominator does not change the signs.
Step 3
Exam Tip
(3) से गुणा करने पर \(6\leq x+1<15\) और \(5\leq x<14\) मिलता है। धनात्मक हर हटाने पर चिन्ह नहीं बदलते।
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कौन सा संख्या रेखा चित्र (x<-5) को दिखाता है?
Which number-line graph represents (x<-5)?
#number-line
#strict-inequality
#representation
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A (-5) पर बंद वृत्त और बाईं ओर छाया
B (-5) पर खुला वृत्त और बाईं ओर छाया
C (-5) पर खुला वृत्त और दाईं ओर छाया
D (-5) पर बंद वृत्त और दाईं ओर छाया
Explanation opens after your attempt
Correct Answer
B. (-5) पर खुला वृत्त और बाईं ओर छाया
Step 1
Concept
In the strict inequality (x<-5), (-5) is not included and smaller numbers are included. So an open circle and left shading are correct.
Step 2
Why this answer is correct
The correct answer is B. (-5) पर खुला वृत्त और बाईं ओर छाया. In the strict inequality (x<-5), (-5) is not included and smaller numbers are included. So an open circle and left shading are correct.
Step 3
Exam Tip
सख्त असमता (x<-5) में (-5) शामिल नहीं है और उससे छोटी संख्याएं शामिल हैं। इसलिए खुला वृत्त और बाईं छाया सही है।
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यदि \(x\in\mathbb{Z}\) और \(3x+2\geq 17\) है तो सबसे छोटा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and \(3x+2\geq 17\), what is the least possible (x)?
#least-integer
#integer-solution
#linear-inequality
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(3x\geq 15\), so \(x\geq 5\). Therefore the least integer solution is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). The inequality gives \(3x\geq 15\), so \(x\geq 5\). Therefore the least integer solution is (5).
Step 3
Exam Tip
असमता से \(3x\geq 15\) और \(x\geq 5\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (5) है।
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किस विकल्प में (x=0) शामिल है लेकिन (x=-3) शामिल नहीं है?
Which option includes (x=0) but excludes (x=-3)?
#endpoint-inclusion
#interval
#concept
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A ([-3,4])
B ((-3,4])
C ([-3,4))
D ((-3,0))
Explanation opens after your attempt
Correct Answer
B. ((-3,4])
Step 1
Concept
In ((-3,4]), (0) is included and (-3) is excluded because of the open endpoint. Inclusion is decided by brackets.
Step 2
Why this answer is correct
The correct answer is B. ((-3,4]). In ((-3,4]), (0) is included and (-3) is excluded because of the open endpoint. Inclusion is decided by brackets.
Step 3
Exam Tip
((-3,4]) में (0) शामिल है और (-3) खुले सिरे के कारण शामिल नहीं है। सिरों के कोष्ठक से समावेशन तय होता है।
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असमता \(-5x+4\leq -16\) का हल कौन सा है?
What is the solution of \(-5x+4\leq -16\)?
#negative-coefficient
#sign-reversal
#linear
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A \(x\leq 4\)
B \(x\geq 4\)
C \(x\leq -4\)
D \(x\geq -4\)
Explanation opens after your attempt
Correct Answer
B. \(x\geq 4\)
Step 1
Concept
From \(-5x\leq -20\), we get \(x\geq 4\). Reversing the sign is necessary when dividing by a negative coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 4\). From \(-5x\leq -20\), we get \(x\geq 4\). Reversing the sign is necessary when dividing by a negative coefficient.
Step 3
Exam Tip
\(-5x\leq -20\) से \(x\geq 4\) मिलता है। ऋणात्मक गुणांक से भाग देने पर चिन्ह पलटना आवश्यक है।
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यदि (4x-7) का मान (13) से अधिक नहीं है तो (x) के लिए सही हल कौन सा है?
If the value of (4x-7) is not greater than (13), which solution for (x) is correct?
#word-translation
#not-greater-than
#solution
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A \(x\geq 5\)
B (x>5)
C \(x\leq 5\)
D (x<5)
Explanation opens after your attempt
Correct Answer
C. \(x\leq 5\)
Step 1
Concept
Not greater than means \(4x-7\leq 13\). This gives \(4x\leq 20\), hence \(x\leq 5\).
Step 2
Why this answer is correct
The correct answer is C. \(x\leq 5\). Not greater than means \(4x-7\leq 13\). This gives \(4x\leq 20\), hence \(x\leq 5\).
Step 3
Exam Tip
अधिक नहीं है का अर्थ \(4x-7\leq 13\) है। इससे \(4x\leq 20\) और \(x\leq 5\) मिलता है।
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कौन सा कथन ((2,7)) अंतराल का सही अर्थ है?
Which statement correctly means the interval ((2,7))?
#open-interval
#notation
#inequality-form
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A \(2\leq x\leq 7\)
B (2<x<7)
C \(2\leq x<7\)
D \(2<x\leq 7\)
Explanation opens after your attempt
Correct Answer
B. (2<x<7)
Step 1
Concept
In the open interval ((2,7)), both endpoints are excluded. Therefore (2<x<7) is correct.
Step 2
Why this answer is correct
The correct answer is B. (2<x<7). In the open interval ((2,7)), both endpoints are excluded. Therefore (2<x<7) is correct.
Step 3
Exam Tip
खुले अंतराल ((2,7)) में दोनों सिरे शामिल नहीं होते। इसलिए (2<x<7) सही है।
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असमता (3(2-x)>x+10) का हल कौन सा है?
What is the solution of (3(2-x)>x+10)?
#bracket-inequality
#negative-division
#solution
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A (x<-1)
B (x>-1)
C (x<1)
D (x>1)
Explanation opens after your attempt
Step 1
Concept
From (6-3x>x+10), we get (-4x>4), hence (x<-1). Reverse the sign when dividing by negative (-4).
Step 2
Why this answer is correct
The correct answer is A. (x<-1). From (6-3x>x+10), we get (-4x>4), hence (x<-1). Reverse the sign when dividing by negative (-4).
Step 3
Exam Tip
(6-3x>x+10) से (-4x>4) और (x<-1) मिलता है। ऋणात्मक (-4) से भाग देने पर चिन्ह पलटें।
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यदि \(x\in\mathbb{R}\) और \(x+4\geq 0\) तथा (2x-1<9) है तो संयुक्त हल कौन सा है?
If \(x\in\mathbb{R}\) and \(x+4\geq 0\) and (2x-1<9), what is the combined solution?
#system-of-inequalities
#intersection
#interval
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A ([-4,5))
B ((-4,5])
C ([-4,5])
D ((-4,5))
Explanation opens after your attempt
Correct Answer
A. ([-4,5))
Step 1
Concept
The first inequality gives \(x\geq -4\), and the second gives (x<5). Their intersection is ([-4,5)).
Step 2
Why this answer is correct
The correct answer is A. ([-4,5)). The first inequality gives \(x\geq -4\), and the second gives (x<5). Their intersection is ([-4,5)).
Step 3
Exam Tip
पहली असमता से \(x\geq -4\) और दूसरी से (x<5) मिलता है। प्रतिच्छेद ([-4,5)) है।
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असमता \(\frac{x-4}{-2}\geq 3\) का हल कौन सा है?
What is the solution of \(\frac{x-4}{-2}\geq 3\)?
#negative-denominator
#sign-reversal
#fractional-inequality
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A \(x\geq -2\)
B \(x\leq -2\)
C \(x\geq 10\)
D \(x\leq 10\)
Explanation opens after your attempt
Correct Answer
B. \(x\leq -2\)
Step 1
Concept
Multiplying by (-2) reverses the sign and gives \(x-4\leq -6\). Therefore \(x\leq -2\).
Step 2
Why this answer is correct
The correct answer is B. \(x\leq -2\). Multiplying by (-2) reverses the sign and gives \(x-4\leq -6\). Therefore \(x\leq -2\).
Step 3
Exam Tip
(-2) से गुणा करने पर चिन्ह पलटकर \(x-4\leq -6\) मिलता है। इसलिए \(x\leq -2\) है।
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यदि \(x\in\mathbb{Z}\) और \(-3\leq \frac{x}{2}<4\) है तो हल समुच्चय कौन सा है?
If \(x\in\mathbb{Z}\) and \(-3\leq \frac{x}{2}<4\), what is the solution set?
#integer-solution
#compound-fraction
#solution-set
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A ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7})
B ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8})
C ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8})
D ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7})
Step 1
Concept
Multiplying by (2) gives \(-6\leq x<8\). Therefore the integer solutions are from (-6) to (7).
Step 2
Why this answer is correct
The correct answer is A. ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}). Multiplying by (2) gives \(-6\leq x<8\). Therefore the integer solutions are from (-6) to (7).
Step 3
Exam Tip
(2) से गुणा करने पर \(-6\leq x<8\) मिलता है। इसलिए पूर्णांक हल (-6) से (7) तक हैं।
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किस असमता का हल कोई वास्तविक संख्या नहीं है?
Which inequality has no real-number solution?
#no-solution
#identity-check
#linear-inequality
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A (x+2>x+5)
B (x+2<x+5)
C \(x+2\leq x+5\)
D \(x+2\geq x+2\)
Explanation opens after your attempt
Correct Answer
A. (x+2>x+5)
Step 1
Concept
From (x+2>x+5), we get (2>5), which is false. If variables cancel and a false statement remains, there is no solution.
Step 2
Why this answer is correct
The correct answer is A. (x+2>x+5). From (x+2>x+5), we get (2>5), which is false. If variables cancel and a false statement remains, there is no solution.
Step 3
Exam Tip
(x+2>x+5) से (2>5) मिलता है जो असत्य है। जब चर कटकर झूठा कथन आए तो कोई हल नहीं होता।
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किस असमता का हल सभी वास्तविक संख्याएं हैं?
Which inequality has all real numbers as its solution?
#all-real-solutions
#identity
#linear-inequality
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A (2x+1>2x+3)
B \(5x-4\leq 5x+2\)
C (3x+7<3x-1)
D (x-6>x+6)
Explanation opens after your attempt
Correct Answer
B. \(5x-4\leq 5x+2\)
Step 1
Concept
From \(5x-4\leq 5x+2\), we get \(-4\leq 2\), which is always true. If a true constant statement remains, all real numbers are solutions.
Step 2
Why this answer is correct
The correct answer is B. \(5x-4\leq 5x+2\). From \(5x-4\leq 5x+2\), we get \(-4\leq 2\), which is always true. If a true constant statement remains, all real numbers are solutions.
Step 3
Exam Tip
\(5x-4\leq 5x+2\) से \(-4\leq 2\) मिलता है जो हमेशा सत्य है। सत्य स्थिर कथन आने पर सभी वास्तविक संख्याएं हल होती हैं।
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यदि (x) एक वास्तविक संख्या है और \(-1<\frac{2x-3}{5}\leq 3\) है तो (x) का हल कौन सा है?
If (x) is a real number and \(-1<\frac{2x-3}{5}\leq 3\), what is the solution for (x)?
#compound-fraction
#real-solution
#interval
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A \(-1<x\leq 9\)
B \(-1\leq x<9\)
C \(1<x\leq 9\)
D (-1<x<9)
Explanation opens after your attempt
Correct Answer
A. \(-1<x\leq 9\)
Step 1
Concept
Multiplying by (5) gives \(-5<2x-3\leq 15\). This gives \(-1<x\leq 9\).
Step 2
Why this answer is correct
The correct answer is A. \(-1<x\leq 9\). Multiplying by (5) gives \(-5<2x-3\leq 15\). This gives \(-1<x\leq 9\).
Step 3
Exam Tip
(5) से गुणा करने पर \(-5<2x-3\leq 15\) मिलता है। इससे \(-1<x\leq 9\) प्राप्त होता है।
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कौन सा विकल्प \(x\leq -4\) या (x>1) का सही अंतराल रूप है?
Which option is the correct interval form of \(x\leq -4\) or (x>1)?
#union
#interval-notation
#endpoint
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A ((-\infty,-4]\cup\(1,\infty\))
B (\(-\infty,-4\)\cup[1,\infty))
C ([-4,1))
D ((-4,1])
Explanation opens after your attempt
Correct Answer
A. ((-\infty,-4]\cup\(1,\infty\))
Step 1
Concept
For or, take the union of the two separate parts. (-4) is included and (1) is not included.
Step 2
Why this answer is correct
The correct answer is A. ((-\infty,-4]\cup\(1,\infty\)). For or, take the union of the two separate parts. (-4) is included and (1) is not included.
Step 3
Exam Tip
या में दोनों अलग भागों का संघ लिया जाता है। (-4) शामिल है और (1) शामिल नहीं है।
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एक परीक्षा में उत्तीर्ण होने के लिए अंक (40) से कम नहीं होने चाहिए। यदि अंक (m) हैं तो सही असमता कौन सी है?
To pass an exam, marks must not be less than (40). If the marks are (m), which inequality is correct?
#word-problem
#not-less-than
#real-life-inequality
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A (m>40)
B \(m\geq 40\)
C (m<40)
D \(m\leq 40\)
Explanation opens after your attempt
Correct Answer
B. \(m\geq 40\)
Step 1
Concept
Must not be less than (40) means (40) or more. Therefore \(m\geq 40\) is the correct inequality.
Step 2
Why this answer is correct
The correct answer is B. \(m\geq 40\). Must not be less than (40) means (40) or more. Therefore \(m\geq 40\) is the correct inequality.
Step 3
Exam Tip
कम नहीं होने चाहिए का अर्थ (40) या उससे अधिक है। इसलिए \(m\geq 40\) सही असमता है।
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असमता (2x-3<5x+12) का हल कौन सा है?
What is the solution of (2x-3<5x+12)?
#linear-inequality
#variables-both-sides
#solution
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A (x>-5)
B (x<-5)
C (x>5)
D (x<5)
Explanation opens after your attempt
Step 1
Concept
From (2x-3<5x+12), we get (-15<3x). Hence (x>-5).
Step 2
Why this answer is correct
The correct answer is A. (x>-5). From (2x-3<5x+12), we get (-15<3x). Hence (x>-5).
Step 3
Exam Tip
(2x-3<5x+12) से (-15<3x) मिलता है। अतः (x>-5) है।
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यदि \(x\in[0,6\)) है तो निम्न में से कौन सा मान शामिल नहीं है?
If \(x\in[0,6\)), which value is not included?
#interval-membership
#endpoint
#concept
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A (x=0)
B (x=5)
C (x=6)
D \(x=\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
In ([0,6)), (0) is included but (6) is not included. A round bracket shows an open endpoint.
Step 2
Why this answer is correct
The correct answer is C. (x=6). In ([0,6)), (0) is included but (6) is not included. A round bracket shows an open endpoint.
Step 3
Exam Tip
([0,6)) में (0) शामिल है लेकिन (6) शामिल नहीं है। गोल कोष्ठक खुले सिरे को दिखाता है।
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यदि (k>0) और \(a\leq b\) है तो कौन सा निष्कर्ष सही है?
If (k>0) and \(a\leq b\), which conclusion is correct?
#positive-multiplication
#inequality-property
#concept
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A \(ka\geq kb\)
B \(ka\leq kb\)
C (ka=kb)
D \(a+k\geq b+k\)
Explanation opens after your attempt
Correct Answer
B. \(ka\leq kb\)
Step 1
Concept
Multiplying by positive (k) keeps the direction of the inequality unchanged. Therefore \(ka\leq kb\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(ka\leq kb\). Multiplying by positive (k) keeps the direction of the inequality unchanged. Therefore \(ka\leq kb\) is correct.
Step 3
Exam Tip
धनात्मक (k) से गुणा करने पर असमता की दिशा वही रहती है। इसलिए \(ka\leq kb\) सही है।
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असमता \(9-3x\geq 2x-16\) का हल कौन सा है?
What is the solution of \(9-3x\geq 2x-16\)?
#linear-inequality
#both-sides
#solution
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A \(x\leq 5\)
B \(x\geq 5\)
C \(x\leq -5\)
D \(x\geq -5\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 5\)
Step 1
Concept
From \(9-3x\geq 2x-16\), we get \(25\geq 5x\). Hence \(x\leq 5\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 5\). From \(9-3x\geq 2x-16\), we get \(25\geq 5x\). Hence \(x\leq 5\).
Step 3
Exam Tip
\(9-3x\geq 2x-16\) से \(25\geq 5x\) मिलता है। अतः \(x\leq 5\) है।
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कौन सी असमता (4) पर खुला वृत्त और दाईं ओर छाया दिखाती है?
Which inequality shows an open circle at (4) and shading to the right?
#number-line
#open-circle
#representation
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A \(x\geq 4\)
B (x>4)
C \(x\leq 4\)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
An open circle shows that (4) is not included, and right shading shows greater numbers. Therefore (x>4) is correct.
Step 2
Why this answer is correct
The correct answer is B. (x>4). An open circle shows that (4) is not included, and right shading shows greater numbers. Therefore (x>4) is correct.
Step 3
Exam Tip
खुला वृत्त बताता है कि (4) शामिल नहीं है और दाईं छाया बड़ी संख्याएं दिखाती है। इसलिए (x>4) सही है।
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यदि \(x\in\mathbb{R}\) और \(12<4x\leq 28\) है तो सही हल कौन सा है?
If \(x\in\mathbb{R}\) and \(12<4x\leq 28\), which solution is correct?
#compound-inequality
#real-solution
#interval
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A \(3<x\leq 7\)
B \(3\leq x<7\)
C (x<3) या \(x\geq 7\)
D \(x\leq 3\) या (x>7)
Explanation opens after your attempt
Correct Answer
A. \(3<x\leq 7\)
Step 1
Concept
Dividing by (4) gives \(3<x\leq 7\). Dividing by a positive number does not change the signs.
Step 2
Why this answer is correct
The correct answer is A. \(3<x\leq 7\). Dividing by (4) gives \(3<x\leq 7\). Dividing by a positive number does not change the signs.
Step 3
Exam Tip
(4) से भाग देने पर \(3<x\leq 7\) मिलता है। धनात्मक संख्या से भाग देने पर चिन्ह नहीं बदलता।
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यदि \(x\in\mathbb{Z}\) और \(\frac{x-2}{3}\leq -1\) है तो सबसे बड़ा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and \(\frac{x-2}{3}\leq -1\), what is the greatest possible (x)?
#integer-solution
#fractional-inequality
#greatest-value
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A (1)
B (0)
C (-1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (3) gives \(x-2\leq -3\), so \(x\leq -1\). Therefore the greatest integer solution is (-1).
Step 2
Why this answer is correct
The correct answer is C. (-1). Multiplying by (3) gives \(x-2\leq -3\), so \(x\leq -1\). Therefore the greatest integer solution is (-1).
Step 3
Exam Tip
(3) से गुणा करने पर \(x-2\leq -3\) और \(x\leq -1\) मिलता है। इसलिए सबसे बड़ा पूर्णांक हल (-1) है।
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असमता (4(x+2)-3(x-5)\geq 20) का हल कौन सा है?
What is the solution of (4(x+2)-3(x-5)\geq 20)?
#brackets
#linear-inequality
#simplification
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A \(x\geq -3\)
B \(x\leq -3\)
C \(x\geq 3\)
D \(x\leq 3\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -3\)
Step 1
Concept
Simplifying gives \(4x+8-3x+15\geq 20\), that is \(x+23\geq 20\). Therefore \(x\geq -3\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -3\). Simplifying gives \(4x+8-3x+15\geq 20\), that is \(x+23\geq 20\). Therefore \(x\geq -3\).
Step 3
Exam Tip
सरलीकरण से \(4x+8-3x+15\geq 20\) यानी \(x+23\geq 20\) मिलता है। इसलिए \(x\geq -3\) है।
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यदि (x) वास्तविक है और (x-2<4) तथा \(x+5\geq 1\) है तो संयुक्त हल क्या है?
If (x) is real and (x-2<4) and \(x+5\geq 1\), what is the combined solution?
#intersection
#combined-solution
#real-numbers
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A ([-4,6))
B ((-4,6])
C ([-4,6])
D ((-4,6))
Explanation opens after your attempt
Correct Answer
A. ([-4,6))
Step 1
Concept
The first inequality gives (x<6), and the second gives \(x\geq -4\). The combined solution is ([-4,6)).
Step 2
Why this answer is correct
The correct answer is A. ([-4,6)). The first inequality gives (x<6), and the second gives \(x\geq -4\). The combined solution is ([-4,6)).
Step 3
Exam Tip
पहली असमता से (x<6) और दूसरी से \(x\geq -4\) मिलता है। संयुक्त हल ([-4,6)) है।
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किस असमता का हल \(\mathbb{R}\) में (\(-\infty,\infty\)) है?
Which inequality has solution (\(-\infty,\infty\)) in \(\mathbb{R}\)?
#all-real-numbers
#identity
#solution-set
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A (x-1>x+2)
B (2x+3<2x+1)
C \(7x-4\leq 7x+9\)
D (5x+6<5x-8)
Explanation opens after your attempt
Correct Answer
C. \(7x-4\leq 7x+9\)
Step 1
Concept
From \(7x-4\leq 7x+9\), we get \(-4\leq 9\), which is always true. Therefore every real (x) is a solution.
Step 2
Why this answer is correct
The correct answer is C. \(7x-4\leq 7x+9\). From \(7x-4\leq 7x+9\), we get \(-4\leq 9\), which is always true. Therefore every real (x) is a solution.
Step 3
Exam Tip
\(7x-4\leq 7x+9\) से \(-4\leq 9\) मिलता है जो हमेशा सत्य है। इसलिए हर वास्तविक (x) हल है।
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असमता \(-3\leq 2x+1<7\) का पूर्णांक हल समुच्चय कौन सा है?
What is the integer solution set of \(-3\leq 2x+1<7\)?
#integer-set
#compound-inequality
#exam-style
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A ({-2,-1,0,1,2})
B ({-1,0,1,2,3})
C ({-2,-1,0,1,2,3})
D ({-3,-2,-1,0,1,2})
Explanation opens after your attempt
Correct Answer
A. ({-2,-1,0,1,2})
Step 1
Concept
From \(-3\leq 2x+1<7\), we get \(-4\leq 2x<6\), hence \(-2\leq x<3\). The integer solutions are from (-2) to (2).
Step 2
Why this answer is correct
The correct answer is A. ({-2,-1,0,1,2}). From \(-3\leq 2x+1<7\), we get \(-4\leq 2x<6\), hence \(-2\leq x<3\). The integer solutions are from (-2) to (2).
Step 3
Exam Tip
\(-3\leq 2x+1<7\) से \(-4\leq 2x<6\) और \(-2\leq x<3\) मिलता है। पूर्णांक हल (-2) से (2) तक हैं।
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