असमानता (3x-5<10) का हल क्या है?
What is the solution of the inequality (3x-5<10)?
#linear inequalities
#one variable
#algebraic solution
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A (x<5)
B (x>5)
C \(x\leq 5\)
D \(x\geq 5\)
Explanation opens after your attempt
Step 1
Concept
From (3x<15), we get (x<5). In exams, first collect like terms on one side.
Step 2
Why this answer is correct
The correct answer is A. (x<5). From (3x<15), we get (x<5). In exams, first collect like terms on one side.
Step 3
Exam Tip
(3x<15) से (x<5) मिलता है। परीक्षा में समान पदों को पहले एक तरफ करें।
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असमानता \(7-2x\geq 1\) को हल कीजिए।
Solve the inequality \(7-2x\geq 1\).
#linear inequalities
#sign change
#negative coefficient
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A \(x\leq 3\)
B \(x\geq 3\)
C (x<3)
D (x>3)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 3\)
Step 1
Concept
In \(-2x\geq -6\), dividing by a negative number reverses the sign. Hence \(x\leq 3\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 3\). In \(-2x\geq -6\), dividing by a negative number reverses the sign. Hence \(x\leq 3\) is correct.
Step 3
Exam Tip
\(-2x\geq -6\) में ऋणात्मक संख्या से भाग देने पर चिन्ह बदलता है। इसलिए \(x\leq 3\) सही है।
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असमानता \(\frac{x}{4}+2\leq 5\) का हल क्या होगा?
What will be the solution of \(\frac{x}{4}+2\leq 5\)?
#linear inequalities
#fraction
#solution
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A \(x\leq 12\)
B \(x\geq 12\)
C (x<12)
D (x>12)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 12\)
Step 1
Concept
From \(\frac{x}{4}\leq 3\), we get \(x\leq 12\). The sign does not change when the divisor is positive.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 12\). From \(\frac{x}{4}\leq 3\), we get \(x\leq 12\). The sign does not change when the divisor is positive.
Step 3
Exam Tip
\(\frac{x}{4}\leq 3\) से \(x\leq 12\) मिलता है। हर सकारात्मक हो तो चिन्ह नहीं बदलता।
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असमानता (5x+8>3x+20) का हल चुनिए।
Choose the solution of (5x+8>3x+20).
#linear inequalities
#variables both sides
#exam
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A (x>6)
B (x<6)
C \(x\geq 6\)
D \(x\leq 6\)
Explanation opens after your attempt
Step 1
Concept
From (2x>12), we get (x>6). Subtracting the same terms from both sides is safe.
Step 2
Why this answer is correct
The correct answer is A. (x>6). From (2x>12), we get (x>6). Subtracting the same terms from both sides is safe.
Step 3
Exam Tip
(2x>12) से (x>6) मिलता है। दोनों तरफ से समान पद घटाना सुरक्षित होता है।
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असमानता \(4x-9\leq 2x+7\) के लिए सही हल कौन सा है?
Which is the correct solution for \(4x-9\leq 2x+7\)?
#linear inequalities
#both sides
#concept
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A \(x\leq 8\)
B \(x\geq 8\)
C (x<8)
D (x>8)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 8\)
Step 1
Concept
Since \(2x\leq 16\), \(x\leq 8\). The sign changes only when multiplying or dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 8\). Since \(2x\leq 16\), \(x\leq 8\). The sign changes only when multiplying or dividing by a negative number.
Step 3
Exam Tip
\(2x\leq 16\) इसलिए \(x\leq 8\) है। चिन्ह तभी बदलता है जब ऋणात्मक संख्या से गुणा या भाग करें।
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असमानता \(2(x-3)\geq x+4\) का हल क्या है?
What is the solution of \(2(x-3)\geq x+4\)?
#linear inequalities
#brackets
#solution
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A \(x\geq 10\)
B \(x\leq 10\)
C (x>10)
D (x<10)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 10\)
Step 1
Concept
From \(2x-6\geq x+4\), we get \(x\geq 10\). Multiply every term correctly when opening brackets.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 10\). From \(2x-6\geq x+4\), we get \(x\geq 10\). Multiply every term correctly when opening brackets.
Step 3
Exam Tip
\(2x-6\geq x+4\) से \(x\geq 10\) मिलता है। ब्रैकेट खोलते समय हर पद से गुणा करें।
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असमानता (3(x+2)<2(x+7)) को हल कीजिए।
Solve the inequality (3(x+2)<2(x+7)).
#linear inequalities
#expansion
#one variable
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A (x<8)
B (x>8)
C \(x\leq 8\)
D \(x\geq 8\)
Explanation opens after your attempt
Step 1
Concept
From (3x+6<2x+14), we get (x<8). After expansion, keep the (x)-terms together.
Step 2
Why this answer is correct
The correct answer is A. (x<8). From (3x+6<2x+14), we get (x<8). After expansion, keep the (x)-terms together.
Step 3
Exam Tip
(3x+6<2x+14) से (x<8) मिलता है। विस्तार के बाद (x) वाले पद साथ रखें।
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असमानता \(\frac{2x-1}{3}\geq 5\) का हल कौन सा है?
Which is the solution of \(\frac{2x-1}{3}\geq 5\)?
#linear inequalities
#fraction
#denominator
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A \(x\geq 8\)
B \(x\leq 8\)
C (x>8)
D (x<8)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 8\)
Step 1
Concept
From \(2x-1\geq 15\), we get \(2x\geq 16\) and \(x\geq 8\). Removing a positive denominator keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 8\). From \(2x-1\geq 15\), we get \(2x\geq 16\) and \(x\geq 8\). Removing a positive denominator keeps the sign unchanged.
Step 3
Exam Tip
\(2x-1\geq 15\) से \(2x\geq 16\) और \(x\geq 8\) मिलता है। सकारात्मक हर हटाने पर चिन्ह वही रहता है।
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असमानता \(\frac{5-x}{2}>4\) का सही हल क्या है?
What is the correct solution of \(\frac{5-x}{2}>4\)?
#linear inequalities
#fraction
#negative variable
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A (x<-3)
B (x>-3)
C \(x\leq -3\)
D \(x\geq -3\)
Explanation opens after your attempt
Step 1
Concept
From (5-x>8), we get (-x>3) and (x<-3). Remember to reverse the sign when dividing by (-1).
Step 2
Why this answer is correct
The correct answer is A. (x<-3). From (5-x>8), we get (-x>3) and (x<-3). Remember to reverse the sign when dividing by (-1).
Step 3
Exam Tip
(5-x>8) से (-x>3) और (x<-3) मिलता है। (-1) से भाग देने पर चिन्ह बदलना याद रखें।
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असमानता \(2\leq x+5<9\) का हल अंतराल रूप में क्या है?
What is the interval form of the solution of \(2\leq x+5<9\)?
#compound inequality
#interval
#one variable
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A ([-3,4))
B ((-3,4])
C ((-3,4))
D ([-3,4])
Explanation opens after your attempt
Correct Answer
A. ([-3,4))
Step 1
Concept
Subtracting (5) from all parts gives \(-3\leq x<4\). Watch open and closed endpoints carefully.
Step 2
Why this answer is correct
The correct answer is A. ([-3,4)). Subtracting (5) from all parts gives \(-3\leq x<4\). Watch open and closed endpoints carefully.
Step 3
Exam Tip
सभी भागों से (5) घटाने पर \(-3\leq x<4\) मिलता है। बंद और खुले सिरों का ध्यान रखें।
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यदि (x) एक पूर्णांक है और (2x+1<9), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (2x+1<9), what is the greatest possible (x)?
#integer solution
#greatest integer
#inequality
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A (3)
B (4)
C (5)
D (2)
Explanation opens after your attempt
Step 1
Concept
From (2x<8), we get (x<4). The greatest integer less than (4) is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). From (2x<8), we get (x<4). The greatest integer less than (4) is (3).
Step 3
Exam Tip
(2x<8) से (x<4) मिलता है। (4) से छोटा सबसे बड़ा पूर्णांक (3) है।
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यदि (x) एक प्राकृतिक संख्या है और \(3x-2\leq 13\), तो (x) के कितने मान संभव हैं?
If (x) is a natural number and \(3x-2\leq 13\), how many values of (x) are possible?
#natural numbers
#counting solutions
#linear inequality
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A (5)
B (4)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
From \(3x\leq 15\), we get \(x\leq 5\). The natural values are (1,2,3,4,5).
Step 2
Why this answer is correct
The correct answer is A. (5). From \(3x\leq 15\), we get \(x\leq 5\). The natural values are (1,2,3,4,5).
Step 3
Exam Tip
\(3x\leq 15\) से \(x\leq 5\) मिलता है। प्राकृतिक मान (1,2,3,4,5) हैं।
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असमानता \(4x+3\geq 2x-5\) का हल समुच्चय कौन सा है?
Which is the solution set of \(4x+3\geq 2x-5\)?
#solution set
#set notation
#linear inequality
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A \({x:x\geq -4}\)
B \({x:x\leq -4}\)
C ({x:x>-4})
D ({x:x<-4})
Explanation opens after your attempt
Correct Answer
A. \({x:x\geq -4}\)
Step 1
Concept
Since \(2x\geq -8\), \(x\geq -4\). In set form, write the condition on the variable clearly.
Step 2
Why this answer is correct
The correct answer is A. \({x:x\geq -4}\). Since \(2x\geq -8\), \(x\geq -4\). In set form, write the condition on the variable clearly.
Step 3
Exam Tip
\(2x\geq -8\) इसलिए \(x\geq -4\) है। समुच्चय रूप में चर की शर्त साफ लिखें।
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असमानता \(6-5x\leq 16\) को हल करने पर क्या मिलता है?
What do we get after solving \(6-5x\leq 16\)?
#negative coefficient
#sign reversal
#linear inequality
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A \(x\geq -2\)
B \(x\leq -2\)
C (x>-2)
D (x<-2)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -2\)
Step 1
Concept
In \(-5x\leq 10\), dividing by (-5) gives \(x\geq -2\). Division by a negative number reverses the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -2\). In \(-5x\leq 10\), dividing by (-5) gives \(x\geq -2\). Division by a negative number reverses the sign.
Step 3
Exam Tip
\(-5x\leq 10\) में (-5) से भाग देने पर \(x\geq -2\) होता है। ऋणात्मक भाग से चिन्ह पलटता है।
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असमानता (8x-3<5x+12) का सही हल चुनिए।
Choose the correct solution of (8x-3<5x+12).
#linear inequality
#boundary point
#variables both sides
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A (x<5)
B (x>5)
C \(x\leq 5\)
D \(x\geq 5\)
Explanation opens after your attempt
Step 1
Concept
From (3x<15), we get (x<5). The boundary point (5) is not included.
Step 2
Why this answer is correct
The correct answer is A. (x<5). From (3x<15), we get (x<5). The boundary point (5) is not included.
Step 3
Exam Tip
(3x<15) से (x<5) मिलता है। सीमा बिंदु (5) शामिल नहीं है।
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असमानता (11-4x>3) का हल क्या है?
What is the solution of (11-4x>3)?
#linear inequality
#negative division
#strict inequality
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A (x<2)
B (x>2)
C \(x\leq 2\)
D \(x\geq 2\)
Explanation opens after your attempt
Step 1
Concept
In (-4x>-8), dividing by (-4) gives (x<2). The strict sign means the boundary is not included.
Step 2
Why this answer is correct
The correct answer is A. (x<2). In (-4x>-8), dividing by (-4) gives (x<2). The strict sign means the boundary is not included.
Step 3
Exam Tip
(-4x>-8) में (-4) से भाग देने पर (x<2) मिलता है। खुले चिन्ह का अर्थ सीमा शामिल नहीं है।
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किस (x) के लिए (5(2x-1)\leq 3x+16) सत्य है?
For which (x) is (5(2x-1)\leq 3x+16) true?
#brackets
#linear inequality
#solution set
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A \(x\leq 3\)
B \(x\geq 3\)
C (x<3)
D (x>3)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 3\)
Step 1
Concept
From \(10x-5\leq 3x+16\), we get \(7x\leq 21\) and \(x\leq 3\). Expand and then simplify.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 3\). From \(10x-5\leq 3x+16\), we get \(7x\leq 21\) and \(x\leq 3\). Expand and then simplify.
Step 3
Exam Tip
\(10x-5\leq 3x+16\) से \(7x\leq 21\) और \(x\leq 3\) मिलता है। विस्तार के बाद सरल करें।
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असमानता (2(3x+4)>4x+18) का हल क्या है?
What is the solution of (2(3x+4)>4x+18)?
#linear inequality
#expansion
#strict solution
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A (x>5)
B (x<5)
C \(x\geq 5\)
D \(x\leq 5\)
Explanation opens after your attempt
Step 1
Concept
From (6x+8>4x+18), we get (2x>10) and (x>5). A strict inequality does not include equality.
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (6x+8>4x+18), we get (2x>10) and (x>5). A strict inequality does not include equality.
Step 3
Exam Tip
(6x+8>4x+18) से (2x>10) और (x>5) मिलता है। सख्त असमानता में बराबरी नहीं आती।
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असमानता \(\frac{x+3}{5}<2\) का हल कौन सा है?
Which is the solution of \(\frac{x+3}{5}<2\)?
#fractional inequality
#positive denominator
#solution
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A (x<7)
B (x>7)
C \(x\leq 7\)
D \(x\geq 7\)
Explanation opens after your attempt
Step 1
Concept
From (x+3<10), we get (x<7). Multiplying by a positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<7). From (x+3<10), we get (x<7). Multiplying by a positive denominator does not change the sign.
Step 3
Exam Tip
(x+3<10) से (x<7) मिलता है। सकारात्मक हर से गुणा करने पर चिन्ह नहीं बदलता।
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असमानता \(\frac{3x+2}{4}\geq \frac{x+6}{2}\) का हल क्या है?
What is the solution of \(\frac{3x+2}{4}\geq \frac{x+6}{2}\)?
#fractional inequality
#lcm
#variables both sides
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A \(x\geq 10\)
B \(x\leq 10\)
C (x>10)
D (x<10)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 10\)
Step 1
Concept
Multiplying by (4) gives \(3x+2\geq 2x+12\). Hence \(x\geq 10\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 10\). Multiplying by (4) gives \(3x+2\geq 2x+12\). Hence \(x\geq 10\) is correct.
Step 3
Exam Tip
(4) से गुणा करने पर \(3x+2\geq 2x+12\) मिलता है। अतः \(x\geq 10\) सही है।
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असमानता \(\frac{x-1}{3}+\frac{x+2}{2}\leq 4\) का हल ज्ञात कीजिए।
Find the solution of \(\frac{x-1}{3}+\frac{x+2}{2}\leq 4\).
#linear inequality
#fractions
#lcm
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A \(x\leq \frac{16}{5}\)
B \(x\geq \frac{16}{5}\)
C \(x<\frac{16}{5}\)
D \(x>\frac{16}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{16}{5}\)
Step 1
Concept
Multiplying by (6) gives \(2x-2+3x+6\leq 24\). So \(5x\leq 16\) and \(x\leq \frac{16}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{16}{5}\). Multiplying by (6) gives \(2x-2+3x+6\leq 24\). So \(5x\leq 16\) and \(x\leq \frac{16}{5}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(2x-2+3x+6\leq 24\) मिलता है। इसलिए \(5x\leq 16\) और \(x\leq \frac{16}{5}\) है।
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असमानता \(\frac{2x+5}{3}-1>4\) का हल क्या होगा?
What will be the solution of \(\frac{2x+5}{3}-1>4\)?
#fractional inequality
#strict
#exam
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A (x>5)
B (x<5)
C \(x\geq 5\)
D \(x\leq 5\)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{2x+5}{3}>5\), we get (2x+5>15). Therefore (x>5).
Step 2
Why this answer is correct
The correct answer is A. (x>5). From \(\frac{2x+5}{3}>5\), we get (2x+5>15). Therefore (x>5).
Step 3
Exam Tip
\(\frac{2x+5}{3}>5\) से (2x+5>15) मिलता है। अतः (x>5) है।
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असमानता \(15\leq 4x-1\) को सरल करने पर सही कथन कौन सा है?
Which statement is correct after simplifying \(15\leq 4x-1\)?
#linear inequality
#reverse reading
#concept
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A \(x\geq 4\)
B \(x\leq 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 4\)
Step 1
Concept
From \(16\leq 4x\), we get \(4\leq x\), that is \(x\geq 4\). Keep the order correct when reading from the left.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 4\). From \(16\leq 4x\), we get \(4\leq x\), that is \(x\geq 4\). Keep the order correct when reading from the left.
Step 3
Exam Tip
\(16\leq 4x\) से \(4\leq x\) अर्थात \(x\geq 4\) मिलता है। बाईं तरफ से पढ़ते समय क्रम को ठीक रखें।
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असमानता \(2x+7\geq 19\) को अंतराल रूप में लिखिए।
Write the solution of \(2x+7\geq 19\) in interval form.
#interval notation
#closed endpoint
#linear inequality
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? Hint Small clue
A \([6,\infty\))
B (\(6,\infty\))
C (\(-\infty,6]\)
D (\(-\infty,6\))
Explanation opens after your attempt
Correct Answer
A. \([6,\infty\))
Step 1
Concept
From \(2x\geq 12\), we get \(x\geq 6\). Since equality is included, write (6) with a closed bracket.
Step 2
Why this answer is correct
The correct answer is A. \([6,\infty\)). From \(2x\geq 12\), we get \(x\geq 6\). Since equality is included, write (6) with a closed bracket.
Step 3
Exam Tip
\(2x\geq 12\) से \(x\geq 6\) मिलता है। बराबरी होने पर (6) को बंद कोष्ठक से लिखते हैं।
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असमानता \(-2x+5\geq 11\) का अंतराल रूप क्या है?
What is the interval form of \(-2x+5\geq 11\)?
#interval notation
#negative coefficient
#closed endpoint
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A (\(-\infty,-3]\)
B \([-3,\infty\))
C (\(-\infty,-3\))
D (\(-3,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,-3]\)
Step 1
Concept
From \(-2x\geq 6\), we get \(x\leq -3\). Dividing by a negative number reverses the direction.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-3]\). From \(-2x\geq 6\), we get \(x\leq -3\). Dividing by a negative number reverses the direction.
Step 3
Exam Tip
\(-2x\geq 6\) से \(x\leq -3\) मिलता है। ऋणात्मक से भाग देने पर दिशा बदलती है।
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कौन सा मान असमानता (4x-6>10) को संतुष्ट करता है?
Which value satisfies the inequality (4x-6>10)?
#checking solution
#value substitution
#linear inequality
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A (x=5)
B (x=4)
C (x=3)
D (x=2)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (4x>16) and (x>4). Among the options, only (5) satisfies this condition.
Step 2
Why this answer is correct
The correct answer is A. (x=5). The inequality gives (4x>16) and (x>4). Among the options, only (5) satisfies this condition.
Step 3
Exam Tip
असमानता से (4x>16) और (x>4) मिलता है। दिए गए विकल्पों में केवल (5) इस शर्त को मानता है।
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कौन सा मान असमानता \(12-3x\leq 0\) का हल है?
Which value is a solution of \(12-3x\leq 0\)?
#solution checking
#boundary value
#inequality
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A (x=4)
B (x=3)
C (x=2)
D (x=1)
Explanation opens after your attempt
Step 1
Concept
From \(12\leq 3x\), we get \(x\geq 4\). Among the options, (4) is correct because equality is included.
Step 2
Why this answer is correct
The correct answer is A. (x=4). From \(12\leq 3x\), we get \(x\geq 4\). Among the options, (4) is correct because equality is included.
Step 3
Exam Tip
\(12\leq 3x\) से \(x\geq 4\) मिलता है। दिए गए विकल्पों में (4) सही है क्योंकि बराबरी शामिल है।
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असमानता \(2x-3\leq x+1\) के हल में (x=4) क्यों शामिल है?
Why is (x=4) included in the solution of \(2x-3\leq x+1\)?
#conceptual
#equality included
#linear inequality
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A क्योंकि \(x\leq 4\) / Because \(x\leq 4\)
B क्योंकि (x<4) / Because (x<4)
C क्योंकि (x>4) / Because (x>4)
D क्योंकि \(x\geq 4\) / Because \(x\geq 4\)
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(x\leq 4\) / Because \(x\leq 4\)
Step 1
Concept
The solution is \(x\leq 4\), so (x=4) is included. In \(\leq\), equality is also valid.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(x\leq 4\) / Because \(x\leq 4\). The solution is \(x\leq 4\), so (x=4) is included. In \(\leq\), equality is also valid.
Step 3
Exam Tip
हल \(x\leq 4\) है इसलिए (x=4) शामिल है। \(\leq\) में बराबरी भी मान्य होती है।
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असमानता (6x+1>6x-5) के बारे में सही निष्कर्ष क्या है?
What is the correct conclusion about (6x+1>6x-5)?
#identity inequality
#all real numbers
#reasoning
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A सभी वास्तविक (x) / All real (x)
B कोई हल नहीं / No solution
C केवल (x>1) / Only (x>1)
D केवल (x<-5) / Only (x<-5)
Explanation opens after your attempt
Correct Answer
A. सभी वास्तविक (x) / All real (x)
Step 1
Concept
Subtracting (6x) from both sides gives (1>-5), which is always true. Therefore all real (x) are solutions.
Step 2
Why this answer is correct
The correct answer is A. सभी वास्तविक (x) / All real (x). Subtracting (6x) from both sides gives (1>-5), which is always true. Therefore all real (x) are solutions.
Step 3
Exam Tip
दोनों तरफ से (6x) घटाने पर (1>-5) मिलता है जो हमेशा सत्य है। इसलिए सभी वास्तविक (x) हल हैं।
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असमानता (4x+9<4x+2) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for (4x+9<4x+2)?
#no solution
#contradiction
#linear inequality
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A कोई हल नहीं / No solution
B सभी वास्तविक (x) / All real (x)
C (x<7)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Subtracting (4x) from both sides gives (9<2), which is false. Hence there is no solution.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Subtracting (4x) from both sides gives (9<2), which is false. Hence there is no solution.
Step 3
Exam Tip
दोनों तरफ से (4x) घटाने पर (9<2) मिलता है जो असत्य है। अतः कोई हल नहीं है।
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यदि (a>0) और (ax+b<c), तो (x) के लिए सही रूप कौन सा है?
If (a>0) and (ax+b<c), which form for (x) is correct?
#parameter
#positive coefficient
#general form
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A \(x<\frac{c-b}{a}\)
B \(x>\frac{c-b}{a}\)
C \(x\leq \frac{c-b}{a}\)
D \(x\geq \frac{c-b}{a}\)
Explanation opens after your attempt
Correct Answer
A. \(x<\frac{c-b}{a}\)
Step 1
Concept
First subtract (b) to get (ax<c-b). Since (a>0), the sign does not change on division.
Step 2
Why this answer is correct
The correct answer is A. \(x<\frac{c-b}{a}\). First subtract (b) to get (ax<c-b). Since (a>0), the sign does not change on division.
Step 3
Exam Tip
पहले (b) घटाकर (ax<c-b) मिलता है। (a>0) होने से भाग देने पर चिन्ह नहीं बदलता।
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एक संख्या का (4) गुना (28) से कम है। इस कथन का सही असमानता रूप क्या है?
Four times a number is less than (28). What is the correct inequality form?
#word problem
#translation
#linear inequality
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A (4x<28)
B (4x>28)
C (x+4<28)
D (x-4<28)
Explanation opens after your attempt
Correct Answer
A. (4x<28)
Step 1
Concept
Let the number be (x), so four times it is (4x). The phrase less than uses the sign (<).
Step 2
Why this answer is correct
The correct answer is A. (4x<28). Let the number be (x), so four times it is (4x). The phrase less than uses the sign (<).
Step 3
Exam Tip
किसी संख्या को (x) मानें तो उसका (4) गुना (4x) है। कम है का चिन्ह (<) होता है।
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किसी संख्या में (7) जोड़ने पर परिणाम (20) से अधिक नहीं है। सही हल क्या है?
When (7) is added to a number, the result is not more than (20). What is the correct solution?
#word problem
#not more than
#solution
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A \(x\leq 13\)
B \(x\geq 13\)
C (x<13)
D (x>13)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 13\)
Step 1
Concept
The statement gives \(x+7\leq 20\). Therefore \(x\leq 13\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 13\). The statement gives \(x+7\leq 20\). Therefore \(x\leq 13\) is correct.
Step 3
Exam Tip
कथन \(x+7\leq 20\) देता है। अतः \(x\leq 13\) सही है।
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यदि किसी संख्या का (3) गुना (5) घटाने पर कम से कम (16) है, तो हल क्या है?
If three times a number decreased by (5) is at least (16), what is the solution?
#word problem
#at least
#linear inequality
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A \(x\geq 7\)
B \(x\leq 7\)
C (x>7)
D (x<7)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 7\)
Step 1
Concept
The statement gives \(3x-5\geq 16\). This gives \(3x\geq 21\) and \(x\geq 7\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 7\). The statement gives \(3x-5\geq 16\). This gives \(3x\geq 21\) and \(x\geq 7\).
Step 3
Exam Tip
कथन \(3x-5\geq 16\) देता है। इससे \(3x\geq 21\) और \(x\geq 7\) मिलता है।
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रवि के पास (50) रुपये हैं। वह (8) रुपये वाली कॉपियां खरीदता है और कम से कम (10) रुपये बचाना चाहता है। अधिकतम कॉपियां कितनी खरीद सकता है?
Ravi has (50) rupees. He buys notebooks costing (8) rupees each and wants to save at least (10) rupees. What is the maximum number of notebooks he can buy?
#word problem
#maximum integer
#linear inequality
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A (5)
B (4)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The condition is \(50-8x\geq 10\), giving \(x\leq 5\). The maximum whole number is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). The condition is \(50-8x\geq 10\), giving \(x\leq 5\). The maximum whole number is (5).
Step 3
Exam Tip
शर्त \(50-8x\geq 10\) है जिससे \(x\leq 5\) मिलता है। अधिकतम पूर्ण संख्या (5) है।
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एक परीक्षा में पास होने के लिए कम से कम (40) अंक चाहिए। यदि \(x+12\geq 40\), तो (x) का न्यूनतम मान क्या है?
At least (40) marks are needed to pass an exam. If \(x+12\geq 40\), what is the minimum value of (x)?
#word problem
#minimum value
#at least
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A (28)
B (27)
C (29)
D (30)
Explanation opens after your attempt
Step 1
Concept
From \(x+12\geq 40\), we get \(x\geq 28\). The minimum value is the boundary point (28).
Step 2
Why this answer is correct
The correct answer is A. (28). From \(x+12\geq 40\), we get \(x\geq 28\). The minimum value is the boundary point (28).
Step 3
Exam Tip
\(x+12\geq 40\) से \(x\geq 28\) मिलता है। न्यूनतम मान सीमा बिंदु (28) है।
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असमानता (2(x+1)-3(x-2)<10) का हल क्या है?
What is the solution of (2(x+1)-3(x-2)<10)?
#brackets
#negative variable
#linear inequality
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A (x>-2)
B (x<-2)
C \(x\geq -2\)
D \(x\leq -2\)
Explanation opens after your attempt
Step 1
Concept
Simplifying gives (2x+2-3x+6<10), that is (-x+8<10). So (-x<2) and (x>-2).
Step 2
Why this answer is correct
The correct answer is A. (x>-2). Simplifying gives (2x+2-3x+6<10), that is (-x+8<10). So (-x<2) and (x>-2).
Step 3
Exam Tip
सरल करने पर (2x+2-3x+6<10) यानी (-x+8<10) मिलता है। इसलिए (-x<2) और (x>-2) है।
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असमानता (4-(x-3)\geq 2x+1) को हल कीजिए।
Solve the inequality (4-(x-3)\geq 2x+1).
#brackets
#minus sign
#linear inequality
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A \(x\leq 2\)
B \(x\geq 2\)
C (x<2)
D (x>2)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 2\)
Step 1
Concept
From \(4-x+3\geq 2x+1\), we get \(7-x\geq 2x+1\). Thus \(6\geq 3x\) and \(x\leq 2\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 2\). From \(4-x+3\geq 2x+1\), we get \(7-x\geq 2x+1\). Thus \(6\geq 3x\) and \(x\leq 2\).
Step 3
Exam Tip
\(4-x+3\geq 2x+1\) से \(7-x\geq 2x+1\) मिलता है। इसलिए \(6\geq 3x\) और \(x\leq 2\) है।
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असमानता \(\frac{x}{2}-\frac{x}{3}>1\) का हल क्या है?
What is the solution of \(\frac{x}{2}-\frac{x}{3}>1\)?
#fractional inequality
#lcm
#strict solution
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A (x>6)
B (x<6)
C \(x\geq 6\)
D \(x\leq 6\)
Explanation opens after your attempt
Step 1
Concept
We get \(\frac{x}{6}>1\), so (x>6). Using the least common multiple is useful with fractions.
Step 2
Why this answer is correct
The correct answer is A. (x>6). We get \(\frac{x}{6}>1\), so (x>6). Using the least common multiple is useful with fractions.
Step 3
Exam Tip
\(\frac{x}{6}>1\) मिलता है इसलिए (x>6) है। भिन्नों में लघुत्तम समापवर्त्य लेना उपयोगी है।
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असमानता \(\frac{3x}{5}+2\leq \frac{x}{5}+6\) के लिए (x) का हल क्या है?
What is the solution for (x) in \(\frac{3x}{5}+2\leq \frac{x}{5}+6\)?
#fractional inequality
#variables both sides
#lcm
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A \(x\leq 10\)
B \(x\geq 10\)
C (x<10)
D (x>10)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 10\)
Step 1
Concept
Multiplying by (5) gives \(3x+10\leq x+30\). So \(2x\leq 20\) and \(x\leq 10\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 10\). Multiplying by (5) gives \(3x+10\leq x+30\). So \(2x\leq 20\) and \(x\leq 10\).
Step 3
Exam Tip
(5) से गुणा करने पर \(3x+10\leq x+30\) मिलता है। इसलिए \(2x\leq 20\) और \(x\leq 10\) है।
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असमानता \(0<\frac{x-2}{3}\leq 4\) का हल कौन सा है?
Which is the solution of \(0<\frac{x-2}{3}\leq 4\)?
#compound inequality
#fraction
#interval
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A \(2<x\leq 14\)
B \(2\leq x<14\)
C (x<2) या (x>14) / (x<2) or (x>14)
D (2<x<14)
Explanation opens after your attempt
Correct Answer
A. \(2<x\leq 14\)
Step 1
Concept
Multiplying by (3) gives \(0<x-2\leq 12\). Adding (2) gives \(2<x\leq 14\).
Step 2
Why this answer is correct
The correct answer is A. \(2<x\leq 14\). Multiplying by (3) gives \(0<x-2\leq 12\). Adding (2) gives \(2<x\leq 14\).
Step 3
Exam Tip
(3) से गुणा करने पर \(0<x-2\leq 12\) मिलता है। फिर (2) जोड़कर \(2<x\leq 14\) मिलता है।
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असमानता \(-6\leq 3x<12\) का हल क्या है?
What is the solution of \(-6\leq 3x<12\)?
#compound inequality
#division
#interval
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A \(-2\leq x<4\)
B \(-2<x\leq 4\)
C (-2<x<4)
D \(-2\leq x\leq 4\)
Explanation opens after your attempt
Correct Answer
A. \(-2\leq x<4\)
Step 1
Concept
Dividing all parts by (3) gives \(-2\leq x<4\). Division by a positive number does not change signs.
Step 2
Why this answer is correct
The correct answer is A. \(-2\leq x<4\). Dividing all parts by (3) gives \(-2\leq x<4\). Division by a positive number does not change signs.
Step 3
Exam Tip
सभी भागों को (3) से भाग देने पर \(-2\leq x<4\) मिलता है। सकारात्मक भाग से चिन्ह नहीं बदलता।
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असमानता \(7x-4\geq 3x+20\) और (x) पूर्णांक है। सबसे छोटा संभव (x) क्या है?
For \(7x-4\geq 3x+20\) and integer (x), what is the least possible (x)?
#integer solution
#least value
#linear inequality
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A (6)
B (5)
C (7)
D (4)
Explanation opens after your attempt
Step 1
Concept
From \(4x\geq 24\), we get \(x\geq 6\). Hence the least integer solution is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). From \(4x\geq 24\), we get \(x\geq 6\). Hence the least integer solution is (6).
Step 3
Exam Tip
\(4x\geq 24\) से \(x\geq 6\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (6) है।
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असमानता \(5-2(3x-1)\leq 15\) का हल क्या है?
What is the solution of the inequality \(5-2(3x-1)\leq 15\)?
#linear inequalities
#brackets
#negative coefficient
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A \(x\geq -\frac{4}{3}\)
B \(x\leq -\frac{4}{3}\)
C \(x>-\frac{4}{3}\)
D \(x<-\frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -\frac{4}{3}\)
Step 1
Concept
Simplifying gives \(7-6x\leq 15\). So \(-6x\leq 8\) and \(x\geq -\frac{4}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -\frac{4}{3}\). Simplifying gives \(7-6x\leq 15\). So \(-6x\leq 8\) and \(x\geq -\frac{4}{3}\).
Step 3
Exam Tip
सरल करने पर \(7-6x\leq 15\) मिलता है। इसलिए \(-6x\leq 8\) और \(x\geq -\frac{4}{3}\) है।
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असमानता \(\frac{4x-3}{5}<\frac{x+6}{2}\) का हल चुनिए।
Choose the solution of \(\frac{4x-3}{5}<\frac{x+6}{2}\).
#fractional inequality
#lcm
#variables both sides
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A (x<12)
B (x>12)
C \(x\leq 12\)
D \(x\geq 12\)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (10) gives (8x-6<5x+30). Therefore (3x<36) and (x<12).
Step 2
Why this answer is correct
The correct answer is A. (x<12). Multiplying by (10) gives (8x-6<5x+30). Therefore (3x<36) and (x<12).
Step 3
Exam Tip
(10) से गुणा करने पर (8x-6<5x+30) मिलता है। इसलिए (3x<36) और (x<12) है।
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यदि (x) पूर्णांक है और \(3<2x+1\leq 13\), तो (x) के कितने मान संभव हैं?
If (x) is an integer and \(3<2x+1\leq 13\), how many values of (x) are possible?
#compound inequality
#integer solutions
#counting
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A (5)
B (4)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
From \(2<2x\leq 12\), we get \(1<x\leq 6\). The integer values are (2,3,4,5,6).
Step 2
Why this answer is correct
The correct answer is A. (5). From \(2<2x\leq 12\), we get \(1<x\leq 6\). The integer values are (2,3,4,5,6).
Step 3
Exam Tip
\(2<2x\leq 12\) से \(1<x\leq 6\) मिलता है। पूर्णांक मान (2,3,4,5,6) हैं।
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असमानता (9-4(x+2)>x-14) का सही हल क्या है?
What is the correct solution of (9-4(x+2)>x-14)?
#linear inequality
#brackets
#strict inequality
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A (x<3)
B (x>3)
C \(x\leq 3\)
D \(x\geq 3\)
Explanation opens after your attempt
Step 1
Concept
Simplifying gives (1-4x>x-14). Thus (15>5x) and (x<3).
Step 2
Why this answer is correct
The correct answer is A. (x<3). Simplifying gives (1-4x>x-14). Thus (15>5x) and (x<3).
Step 3
Exam Tip
सरल करने पर (1-4x>x-14) मिलता है। इसलिए (15>5x) और (x<3) है।
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किसी संख्या के (2) गुने से (9) घटाने पर परिणाम (-1) से कम नहीं है। सही हल क्या है?
When (9) is subtracted from twice a number, the result is not less than (-1). What is the correct solution?
#word problem
#not less than
#linear inequality
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A \(x\geq 4\)
B \(x\leq 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 4\)
Step 1
Concept
The statement gives \(2x-9\geq -1\). This gives \(2x\geq 8\) and \(x\geq 4\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 4\). The statement gives \(2x-9\geq -1\). This gives \(2x\geq 8\) and \(x\geq 4\).
Step 3
Exam Tip
कथन \(2x-9\geq -1\) देता है। इससे \(2x\geq 8\) और \(x\geq 4\) मिलता है।
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असमानता \(-3\leq \frac{x+4}{2}<5\) का हल क्या है?
What is the solution of \(-3\leq \frac{x+4}{2}<5\)?
#compound inequality
#fraction
#interval notation
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A \(-10\leq x<6\)
B \(-10<x\leq 6\)
C \(-10\leq x\leq 6\)
D (-10<x<6)
Explanation opens after your attempt
Correct Answer
A. \(-10\leq x<6\)
Step 1
Concept
Multiplying all parts by (2) gives \(-6\leq x+4<10\). Subtracting (4) gives \(-10\leq x<6\).
Step 2
Why this answer is correct
The correct answer is A. \(-10\leq x<6\). Multiplying all parts by (2) gives \(-6\leq x+4<10\). Subtracting (4) gives \(-10\leq x<6\).
Step 3
Exam Tip
सभी भागों को (2) से गुणा करने पर \(-6\leq x+4<10\) मिलता है। फिर (4) घटाकर \(-10\leq x<6\) मिलता है।
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असमानता (2(x-5)+3\geq 3(x-4)-7) का हल कौन सा है?
Which is the solution of (2(x-5)+3\geq 3(x-4)-7)?
#linear inequality
#expansion
#variables both sides
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A \(x\leq 12\)
B \(x\geq 12\)
C (x<12)
D (x>12)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 12\)
Step 1
Concept
Simplifying gives \(2x-7\geq 3x-19\). This gives \(12\geq x\), that is \(x\leq 12\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 12\). Simplifying gives \(2x-7\geq 3x-19\). This gives \(12\geq x\), that is \(x\leq 12\).
Step 3
Exam Tip
सरल करने पर \(2x-7\geq 3x-19\) मिलता है। इससे \(12\geq x\) अर्थात \(x\leq 12\) है।
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