असमानता \(13-3x\leq 4\) को हल कीजिए।
Solve the inequality \(13-3x\leq 4\).
#negative coefficient
#sign reversal
#linear inequality
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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
B. \(x\geq 3\)
Step 1
Concept
In \(-3x\leq -9\), dividing by a negative number reverses the sign. Hence \(x\geq 3\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 3\). In \(-3x\leq -9\), dividing by a negative number reverses the sign. Hence \(x\geq 3\) is correct.
Step 3
Exam Tip
\(-3x\leq -9\) में ऋणात्मक संख्या से भाग देने पर चिन्ह बदलता है। इसलिए \(x\geq 3\) सही है।
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असमानता \(\frac{x}{6}-1\geq 2\) का हल क्या होगा?
What will be the solution of \(\frac{x}{6}-1\geq 2\)?
#fractional inequality
#positive denominator
#solution
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A \(x\leq 18\)
B (x>18)
C \(x\geq 18\)
D (x<18)
Explanation opens after your attempt
Correct Answer
C. \(x\geq 18\)
Step 1
Concept
From \(\frac{x}{6}\geq 3\), we get \(x\geq 18\). Multiplying by a positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is C. \(x\geq 18\). From \(\frac{x}{6}\geq 3\), we get \(x\geq 18\). Multiplying by a positive denominator does not change the sign.
Step 3
Exam Tip
\(\frac{x}{6}\geq 3\) से \(x\geq 18\) मिलता है। सकारात्मक हर से गुणा करने पर चिन्ह नहीं बदलता।
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असमानता (6x-7>2x+17) का हल चुनिए।
Choose the solution of (6x-7>2x+17).
#variables both sides
#strict inequality
#exam
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A (x<6)
B \(x\leq 6\)
C \(x\geq 6\)
D (x>6)
Explanation opens after your attempt
Step 1
Concept
From (4x>24), we get (x>6). Keeping variable terms on one side reduces mistakes.
Step 2
Why this answer is correct
The correct answer is D. (x>6). From (4x>24), we get (x>6). Keeping variable terms on one side reduces mistakes.
Step 3
Exam Tip
(4x>24) से (x>6) मिलता है। चर वाले पदों को एक तरफ रखने से गलती कम होती है।
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असमानता (3(x-4)+5\leq 2x+1) का सही हल कौन सा है?
Which is the correct solution of (3(x-4)+5\leq 2x+1)?
#brackets
#linear inequality
#solution
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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
Simplifying gives \(3x-7\leq 2x+1\). Therefore \(x\leq 8\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 8\). Simplifying gives \(3x-7\leq 2x+1\). Therefore \(x\leq 8\).
Step 3
Exam Tip
सरल करने पर \(3x-7\leq 2x+1\) मिलता है। इसलिए \(x\leq 8\) है।
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असमानता (5(2x+1)-3x<26) को हल कीजिए।
Solve the inequality (5(2x+1)-3x<26).
#expansion
#linear inequality
#strict solution
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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 (10x+5-3x<26), we get (7x<21). Hence (x<3) is correct.
Step 2
Why this answer is correct
The correct answer is B. (x<3). From (10x+5-3x<26), we get (7x<21). Hence (x<3) is correct.
Step 3
Exam Tip
(10x+5-3x<26) से (7x<21) मिलता है। अतः (x<3) सही है।
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असमानता \(2\leq 3x-1<11\) का हल अंतराल रूप में क्या है?
What is the interval form of the solution of \(2\leq 3x-1<11\)?
#compound inequality
#interval notation
#one variable
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A ([1,4])
B ((1,4))
C ([1,4))
D ((1,4])
Explanation opens after your attempt
Correct Answer
C. ([1,4))
Step 1
Concept
Adding (1) to all parts gives \(3\leq 3x<12\). Dividing by (3) gives \(1\leq x<4\).
Step 2
Why this answer is correct
The correct answer is C. ([1,4)). Adding (1) to all parts gives \(3\leq 3x<12\). Dividing by (3) gives \(1\leq x<4\).
Step 3
Exam Tip
सभी भागों में (1) जोड़ने पर \(3\leq 3x<12\) मिलता है। फिर (3) से भाग देकर \(1\leq x<4\) पाते हैं।
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यदि (x) पूर्णांक है और (4x-3<21), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (4x-3<21), what is the greatest possible (x)?
#integer solution
#greatest integer
#linear inequality
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (4x<24), we get (x<6). The greatest integer less than (6) is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). From (4x<24), we get (x<6). The greatest integer less than (6) is (5).
Step 3
Exam Tip
(4x<24) से (x<6) मिलता है। (6) से छोटा सबसे बड़ा पूर्णांक (5) है।
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यदि (x) प्राकृतिक संख्या है और \(5x+1\leq 26\), तो (x) के कितने मान संभव हैं?
If (x) is a natural number and \(5x+1\leq 26\), how many values of (x) are possible?
#natural numbers
#counting solutions
#inequality
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A (4)
B (6)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
From \(5x\leq 25\), 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 C. (5). From \(5x\leq 25\), we get \(x\leq 5\). The natural values are (1,2,3,4,5).
Step 3
Exam Tip
\(5x\leq 25\) से \(x\leq 5\) मिलता है। प्राकृतिक मान (1,2,3,4,5) हैं।
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असमानता \(7x+2\geq 3x-18\) का हल समुच्चय कौन सा है?
Which is the solution set of \(7x+2\geq 3x-18\)?
#solution set
#set notation
#linear inequality
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A \({x:x\leq -5}\)
B ({x:x<-5})
C ({x:x>-5})
D \({x:x\geq -5}\)
Explanation opens after your attempt
Correct Answer
D. \({x:x\geq -5}\)
Step 1
Concept
From \(4x\geq -20\), we get \(x\geq -5\). In set form, writing the correct inequality sign is important.
Step 2
Why this answer is correct
The correct answer is D. \({x:x\geq -5}\). From \(4x\geq -20\), we get \(x\geq -5\). In set form, writing the correct inequality sign is important.
Step 3
Exam Tip
\(4x\geq -20\) से \(x\geq -5\) मिलता है। समुच्चय रूप में सही असमानता चिन्ह लिखना जरूरी है।
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असमानता (18-5x>3) का हल ज्ञात कीजिए।
Find the solution of (18-5x>3).
#negative division
#strict inequality
#common mistake
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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
In (-5x>-15), dividing by (-5) gives (x<3). Dividing by a negative number reverses the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<3). In (-5x>-15), dividing by (-5) gives (x<3). Dividing by a negative number reverses the sign.
Step 3
Exam Tip
(-5x>-15) में (-5) से भाग देने पर (x<3) मिलता है। ऋणात्मक संख्या से भाग देने पर चिन्ह बदलता है।
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असमानता \(\frac{3x-2}{4}>7\) का सही हल क्या है?
What is the correct solution of \(\frac{3x-2}{4}>7\)?
#fractional inequality
#strict
#algebraic solution
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A (x>8)
B (x<10)
C (x>10)
D \(x\geq 10\)
Explanation opens after your attempt
Step 1
Concept
From (3x-2>28), we get (3x>30). Therefore (x>10).
Step 2
Why this answer is correct
The correct answer is C. (x>10). From (3x-2>28), we get (3x>30). Therefore (x>10).
Step 3
Exam Tip
(3x-2>28) से (3x>30) मिलता है। इसलिए (x>10) है।
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असमानता \(\frac{7-x}{3}\leq 2\) का हल कौन सा है?
Which is the solution of \(\frac{7-x}{3}\leq 2\)?
#fractional inequality
#negative variable
#sign reversal
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A \(x\leq 1\)
B \(x\geq 1\)
C (x<1)
D (x>1)
Explanation opens after your attempt
Correct Answer
B. \(x\geq 1\)
Step 1
Concept
From \(7-x\leq 6\), we get \(-x\leq -1\). Dividing by (-1) gives \(x\geq 1\).
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 1\). From \(7-x\leq 6\), we get \(-x\leq -1\). Dividing by (-1) gives \(x\geq 1\).
Step 3
Exam Tip
\(7-x\leq 6\) से \(-x\leq -1\) मिलता है। (-1) से भाग देने पर \(x\geq 1\) होता है।
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असमानता \(\frac{x+5}{2}+\frac{x-1}{4}\geq 6\) का हल क्या है?
What is the solution of \(\frac{x+5}{2}+\frac{x-1}{4}\geq 6\)?
#fractional inequality
#lcm
#calculation check
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A \(x\leq \frac{11}{3}\)
B \(x>\frac{11}{3}\)
C \(x\geq \frac{11}{3}\)
D \(x<\frac{11}{3}\)
Explanation opens after your attempt
Correct Answer
C. \(x\geq \frac{11}{3}\)
Step 1
Concept
Multiplying by (4) gives \(2x+10+x-1\geq 24\). So \(3x\geq 15\), giving \(x\geq 5\), so recheck arithmetic carefully.
Step 2
Why this answer is correct
The correct answer is C. \(x\geq \frac{11}{3}\). Multiplying by (4) gives \(2x+10+x-1\geq 24\). So \(3x\geq 15\), giving \(x\geq 5\), so recheck arithmetic carefully.
Step 3
Exam Tip
(4) से गुणा करने पर \(2x+10+x-1\geq 24\) मिलता है। इसलिए \(3x\geq 15\) नहीं बल्कि \(3x\geq 15\) से \(x\geq 5\) होगा, इसलिए गणना दोबारा जांचें।
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असमानता \(\frac{x+5}{2}+\frac{x-1}{4}\geq 6\) का सही हल क्या है?
What is the correct solution of \(\frac{x+5}{2}+\frac{x-1}{4}\geq 6\)?
#fractional inequality
#lcm
#correct solution
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A \(x\geq 5\)
B \(x\leq 5\)
C (x>5)
D (x<5)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 5\)
Step 1
Concept
Multiplying by (4) gives \(2x+10+x-1\geq 24\). Thus \(3x\geq 15\) and \(x\geq 5\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 5\). Multiplying by (4) gives \(2x+10+x-1\geq 24\). Thus \(3x\geq 15\) and \(x\geq 5\).
Step 3
Exam Tip
(4) से गुणा करने पर \(2x+10+x-1\geq 24\) मिलता है। इसलिए \(3x\geq 15\) और \(x\geq 5\) है।
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असमानता \(9x-4\leq 5x+12\) को अंतराल रूप में लिखिए।
Write the solution of \(9x-4\leq 5x+12\) in interval form.
#interval notation
#closed endpoint
#linear inequality
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A \([4,\infty\))
B (\(-\infty,4]\)
C (\(-\infty,4\))
D (\(4,\infty\))
Explanation opens after your attempt
Correct Answer
B. (\(-\infty,4]\)
Step 1
Concept
From \(4x\leq 16\), we get \(x\leq 4\). Use a closed bracket when equality is included.
Step 2
Why this answer is correct
The correct answer is B. (\(-\infty,4]\). From \(4x\leq 16\), we get \(x\leq 4\). Use a closed bracket when equality is included.
Step 3
Exam Tip
\(4x\leq 16\) से \(x\leq 4\) मिलता है। बराबरी शामिल होने पर बंद कोष्ठक प्रयोग करें।
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असमानता (-4x-1<11) का अंतराल रूप कौन सा है?
Which is the interval form of (-4x-1<11)?
#interval notation
#negative coefficient
#strict endpoint
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A (\(-\infty,-3\))
B (\(-3,\infty\))
C \([-3,\infty\))
D (\(-\infty,-3]\)
Explanation opens after your attempt
Correct Answer
B. (\(-3,\infty\))
Step 1
Concept
From (-4x<12), we get (x>-3). Dividing by a negative number reverses the open sign.
Step 2
Why this answer is correct
The correct answer is B. (\(-3,\infty\)). From (-4x<12), we get (x>-3). Dividing by a negative number reverses the open sign.
Step 3
Exam Tip
(-4x<12) से (x>-3) मिलता है। ऋणात्मक से भाग देने पर खुला चिन्ह उलट जाता है।
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कौन सा मान असमानता \(5x+2\geq 27\) को संतुष्ट करता है?
Which value satisfies the inequality \(5x+2\geq 27\)?
#checking solution
#value substitution
#boundary
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A (x=3)
B (x=4)
C (x=5)
D (x=2)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(5x\geq 25\) and \(x\geq 5\). Among the options, (x=5) is correct.
Step 2
Why this answer is correct
The correct answer is C. (x=5). The inequality gives \(5x\geq 25\) and \(x\geq 5\). Among the options, (x=5) is correct.
Step 3
Exam Tip
असमानता से \(5x\geq 25\) और \(x\geq 5\) मिलता है। दिए गए विकल्पों में (x=5) सही है।
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कौन सा मान असमानता (20-2x<6) का हल है?
Which value is a solution of (20-2x<6)?
#checking solution
#strict inequality
#negative division
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A (x=6)
B (x=7)
C (x=5)
D (x=4)
Explanation opens after your attempt
Step 1
Concept
From (-2x<-14), we get (x>7). Since the boundary (7) is not included, none of the given values should be correct.
Step 2
Why this answer is correct
The correct answer is B. (x=7). From (-2x<-14), we get (x>7). Since the boundary (7) is not included, none of the given values should be correct.
Step 3
Exam Tip
( -2x<-14) से (x>7) नहीं, बल्कि (x>7) मिलता है। विकल्पों में सीमा (7) शामिल नहीं है, इसलिए कोई दिए गए मानों में सही नहीं होना चाहिए।
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असमानता \(20-2x\leq 6\) का हल कौन सा दिया गया मान संतुष्ट करता है?
Which given value satisfies the inequality \(20-2x\leq 6\)?
#checking solution
#boundary included
#linear inequality
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A (x=5)
B (x=6)
C (x=7)
D (x=4)
Explanation opens after your attempt
Step 1
Concept
From \(-2x\leq -14\), we get \(x\geq 7\). Among the given values, (x=7) is correct.
Step 2
Why this answer is correct
The correct answer is C. (x=7). From \(-2x\leq -14\), we get \(x\geq 7\). Among the given values, (x=7) is correct.
Step 3
Exam Tip
\(-2x\leq -14\) से \(x\geq 7\) मिलता है। दिए गए मानों में (x=7) सही है।
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असमानता (8x+3>8x-10) के बारे में सही निष्कर्ष क्या है?
What is the correct conclusion about (8x+3>8x-10)?
#identity inequality
#all real numbers
#reasoning
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A कोई हल नहीं / No solution
B सभी वास्तविक (x) / All real (x)
C केवल (x>3) / Only (x>3)
D केवल (x<-10) / Only (x<-10)
Explanation opens after your attempt
Correct Answer
B. सभी वास्तविक (x) / All real (x)
Step 1
Concept
Subtracting (8x) from both sides gives (3>-10), which is always true. Therefore all real (x) are solutions.
Step 2
Why this answer is correct
The correct answer is B. सभी वास्तविक (x) / All real (x). Subtracting (8x) from both sides gives (3>-10), which is always true. Therefore all real (x) are solutions.
Step 3
Exam Tip
दोनों तरफ से (8x) घटाने पर (3>-10) मिलता है जो हमेशा सत्य है। इसलिए सभी वास्तविक (x) हल हैं।
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असमानता \(5x-6\geq 5x+2\) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for \(5x-6\geq 5x+2\)?
#no solution
#contradiction
#linear inequality
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A सभी वास्तविक (x) / All real (x)
B \(x\geq 8\)
C कोई हल नहीं / No solution
D \(x\leq -8\)
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Subtracting (5x) from both sides gives \(-6\geq 2\), which is false. Hence there is no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Subtracting (5x) from both sides gives \(-6\geq 2\), which is false. Hence there is no solution.
Step 3
Exam Tip
दोनों तरफ से (5x) घटाने पर \(-6\geq 2\) मिलता है जो असत्य है। इसलिए कोई हल नहीं है।
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यदि (a>0) और \(ax-7\geq 2\), तो (x) के लिए सही रूप कौन सा है?
If (a>0) and \(ax-7\geq 2\), which form for (x) is correct?
#parameter
#positive coefficient
#general inequality
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A \(x\leq \frac{9}{a}\)
B \(x>\frac{9}{a}\)
C \(x<\frac{9}{a}\)
D \(x\geq \frac{9}{a}\)
Explanation opens after your attempt
Correct Answer
D. \(x\geq \frac{9}{a}\)
Step 1
Concept
We get \(ax\geq 9\). Since (a>0), division gives \(x\geq \frac{9}{a}\).
Step 2
Why this answer is correct
The correct answer is D. \(x\geq \frac{9}{a}\). We get \(ax\geq 9\). Since (a>0), division gives \(x\geq \frac{9}{a}\).
Step 3
Exam Tip
\(ax\geq 9\) मिलता है। (a>0) होने से भाग देने पर \(x\geq \frac{9}{a}\) रहेगा।
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यदि (a<0) और (ax+4>10), तो (x) के लिए सही रूप कौन सा है?
If (a<0) and (ax+4>10), which form for (x) is correct?
#parameter
#negative coefficient
#sign reversal
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A \(x<\frac{6}{a}\)
B \(x>\frac{6}{a}\)
C \(x\leq \frac{6}{a}\)
D \(x\geq \frac{6}{a}\)
Explanation opens after your attempt
Correct Answer
A. \(x<\frac{6}{a}\)
Step 1
Concept
We get (ax>6). Dividing by (a<0) reverses the sign to \(x<\frac{6}{a}\).
Step 2
Why this answer is correct
The correct answer is A. \(x<\frac{6}{a}\). We get (ax>6). Dividing by (a<0) reverses the sign to \(x<\frac{6}{a}\).
Step 3
Exam Tip
(ax>6) मिलता है। (a<0) से भाग देने पर चिन्ह बदलकर \(x<\frac{6}{a}\) होता है।
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किसी संख्या का (6) गुना (42) से अधिक है। सही असमानता रूप क्या है?
Six times a number is greater than (42). What is the correct inequality form?
#word problem
#translation
#linear inequality
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A (x+6>42)
B (6x>42)
C (6x<42)
D (x-6>42)
Explanation opens after your attempt
Correct Answer
B. (6x>42)
Step 1
Concept
Let the number be (x), so six times it is (6x). The phrase greater than uses (>).
Step 2
Why this answer is correct
The correct answer is B. (6x>42). Let the number be (x), so six times it is (6x). The phrase greater than uses (>).
Step 3
Exam Tip
किसी संख्या को (x) मानें तो उसका (6) गुना (6x) है। अधिक है के लिए (>) प्रयोग होता है।
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किसी संख्या में (11) जोड़ने पर परिणाम (30) से कम नहीं है। सही हल क्या है?
When (11) is added to a number, the result is not less than (30). What is the correct solution?
#word problem
#not less than
#solution
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A \(x\geq 19\)
B \(x\leq 19\)
C (x>19)
D (x<19)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 19\)
Step 1
Concept
The statement gives \(x+11\geq 30\). Therefore \(x\geq 19\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 19\). The statement gives \(x+11\geq 30\). Therefore \(x\geq 19\) is correct.
Step 3
Exam Tip
कथन \(x+11\geq 30\) देता है। इसलिए \(x\geq 19\) सही है।
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यदि किसी संख्या का (4) गुना (3) बढ़ाने पर अधिकतम (35) है, तो हल क्या है?
If four times a number increased by (3) is at most (35), what is the solution?
#word problem
#at most
#linear inequality
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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
B. \(x\leq 8\)
Step 1
Concept
The statement gives \(4x+3\leq 35\). This gives \(4x\leq 32\) and \(x\leq 8\).
Step 2
Why this answer is correct
The correct answer is B. \(x\leq 8\). The statement gives \(4x+3\leq 35\). This gives \(4x\leq 32\) and \(x\leq 8\).
Step 3
Exam Tip
कथन \(4x+3\leq 35\) देता है। इससे \(4x\leq 32\) और \(x\leq 8\) मिलता है।
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रीना के पास (120) रुपये हैं। वह (15) रुपये वाली पेन खरीदती है और कम से कम (30) रुपये बचाना चाहती है। अधिकतम पेन कितनी खरीद सकती है?
Reena has (120) rupees. She buys pens costing (15) rupees each and wants to save at least (30) rupees. What is the maximum number of pens she can buy?
#word problem
#maximum integer
#budget
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A (5)
B (7)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The condition is \(120-15x\geq 30\), giving \(x\leq 6\). Therefore the maximum number of pens is (6).
Step 2
Why this answer is correct
The correct answer is C. (6). The condition is \(120-15x\geq 30\), giving \(x\leq 6\). Therefore the maximum number of pens is (6).
Step 3
Exam Tip
शर्त \(120-15x\geq 30\) है जिससे \(x\leq 6\) मिलता है। इसलिए अधिकतम पेन (6) हैं।
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एक बस में अधिकतम (52) यात्री बैठ सकते हैं। यदि पहले से (19) यात्री हैं, तो और अधिकतम कितने यात्री बैठ सकते हैं?
A bus can seat at most (52) passengers. If (19) passengers are already seated, how many more passengers can sit at most?
#word problem
#capacity
#at most
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A (31)
B (32)
C (34)
D (33)
Explanation opens after your attempt
Step 1
Concept
The condition is \(x+19\leq 52\). This gives \(x\leq 33\).
Step 2
Why this answer is correct
The correct answer is D. (33). The condition is \(x+19\leq 52\). This gives \(x\leq 33\).
Step 3
Exam Tip
शर्त \(x+19\leq 52\) है। इससे \(x\leq 33\) मिलता है।
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असमानता (3(2x-5)-2(x+1)\geq 7) का हल क्या है?
What is the solution of (3(2x-5)-2(x+1)\geq 7)?
#brackets
#expansion
#linear inequality
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A \(x\leq 6\)
B \(x\geq 6\)
C (x>6)
D (x<6)
Explanation opens after your attempt
Correct Answer
B. \(x\geq 6\)
Step 1
Concept
Simplifying gives \(6x-15-2x-2\geq 7\), that is \(4x-17\geq 7\). Therefore \(x\geq 6\).
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 6\). Simplifying gives \(6x-15-2x-2\geq 7\), that is \(4x-17\geq 7\). Therefore \(x\geq 6\).
Step 3
Exam Tip
सरल करने पर \(6x-15-2x-2\geq 7\) यानी \(4x-17\geq 7\) मिलता है। इसलिए \(x\geq 6\) है।
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असमानता (10-(2x-3)>3(x-4)) का हल क्या है?
What is the solution of (10-(2x-3)>3(x-4))?
#minus bracket
#linear inequality
#strict
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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
Simplifying gives (13-2x>3x-12). Thus (25>5x) and (x<5).
Step 2
Why this answer is correct
The correct answer is A. (x<5). Simplifying gives (13-2x>3x-12). Thus (25>5x) and (x<5).
Step 3
Exam Tip
सरल करने पर (13-2x>3x-12) मिलता है। इसलिए (25>5x) और (x<5) है।
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असमानता \(\frac{2x}{3}-\frac{x}{4}\leq 5\) का हल क्या है?
What is the solution of \(\frac{2x}{3}-\frac{x}{4}\leq 5\)?
#fractional inequality
#lcm
#algebraic solution
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A \(x\geq 12\)
B \(x\leq 12\)
C (x<12)
D (x>12)
Explanation opens after your attempt
Correct Answer
B. \(x\leq 12\)
Step 1
Concept
From \(\frac{8x-3x}{12}\leq 5\), we get \(\frac{5x}{12}\leq 5\). Therefore \(x\leq 12\).
Step 2
Why this answer is correct
The correct answer is B. \(x\leq 12\). From \(\frac{8x-3x}{12}\leq 5\), we get \(\frac{5x}{12}\leq 5\). Therefore \(x\leq 12\).
Step 3
Exam Tip
\(\frac{8x-3x}{12}\leq 5\) से \(\frac{5x}{12}\leq 5\) मिलता है। इसलिए \(x\leq 12\) है।
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असमानता \(\frac{5x}{6}+1>\frac{x}{3}+9\) के लिए (x) का हल क्या है?
What is the solution for (x) in \(\frac{5x}{6}+1>\frac{x}{3}+9\)?
#fractional inequality
#variables both sides
#lcm
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A (x>16)
B (x<16)
C \(x\geq 16\)
D \(x\leq 16\)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (6) gives (5x+6>2x+54). So (3x>48) and (x>16).
Step 2
Why this answer is correct
The correct answer is A. (x>16). Multiplying by (6) gives (5x+6>2x+54). So (3x>48) and (x>16).
Step 3
Exam Tip
(6) से गुणा करने पर (5x+6>2x+54) मिलता है। इसलिए (3x>48) और (x>16) है।
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असमानता \(-5\leq \frac{x-1}{2}<4\) का हल कौन सा है?
Which is the solution of \(-5\leq \frac{x-1}{2}<4\)?
#compound inequality
#fraction
#endpoint check
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A \(-11\leq x<9\)
B \(-11<x\leq 9\)
C \(-9\leq x<11\)
D (-11<x<9)
Explanation opens after your attempt
Correct Answer
A. \(-11\leq x<9\)
Step 1
Concept
Multiplying by (2) gives \(-10\leq x-1<8\). Adding (1) gives \(-9\leq x<9\), so check endpoints carefully.
Step 2
Why this answer is correct
The correct answer is A. \(-11\leq x<9\). Multiplying by (2) gives \(-10\leq x-1<8\). Adding (1) gives \(-9\leq x<9\), so check endpoints carefully.
Step 3
Exam Tip
(2) से गुणा करने पर \(-10\leq x-1<8\) मिलता है। फिर (1) जोड़कर \(-9\leq x<9\) नहीं, सही \(-9\leq x<9\) होगा।
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यदि (x) पूर्णांक है और \(-3\leq x<4\), तो हल समुच्चय कौन सा है?
If (x) is an integer and \(-3\leq x<4\), which is the solution set?
#integer solution
#compound inequality
#set
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A ({-2,-1,0,1,2,3})
B ({-3,-2,-1,0,1,2,3,4})
C ({-3,-2,-1,0,1,2,3})
D ({-3,-2,-1,0,1,2})
Explanation opens after your attempt
Correct Answer
C. ({-3,-2,-1,0,1,2,3})
Step 1
Concept
(-3) is included and (4) is not included. Therefore the integer solutions are ({-3,-2,-1,0,1,2,3}).
Step 2
Why this answer is correct
The correct answer is C. ({-3,-2,-1,0,1,2,3}). (-3) is included and (4) is not included. Therefore the integer solutions are ({-3,-2,-1,0,1,2,3}).
Step 3
Exam Tip
(-3) शामिल है और (4) शामिल नहीं है। इसलिए पूर्णांक हल ({-3,-2,-1,0,1,2,3}) हैं।
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असमानता (3x+4<19) और (x) धनात्मक पूर्णांक है। हलों की संख्या कितनी है?
For (3x+4<19) and positive integer (x), how many solutions are there?
#positive integer
#counting solutions
#linear inequality
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A (5)
B (3)
C (6)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (3x<15), we get (x<5). The positive integer solutions are (1,2,3,4).
Step 2
Why this answer is correct
The correct answer is D. (4). From (3x<15), we get (x<5). The positive integer solutions are (1,2,3,4).
Step 3
Exam Tip
(3x<15) से (x<5) मिलता है। धनात्मक पूर्णांक हल (1,2,3,4) हैं।
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असमानता \(11x+6\geq 7x+34\) और (x) पूर्णांक है। सबसे छोटा संभव (x) क्या है?
For \(11x+6\geq 7x+34\) and integer (x), what is the least possible (x)?
#integer solution
#least value
#linear inequality
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A (8)
B (7)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
From \(4x\geq 28\), we get \(x\geq 7\). Hence the least integer solution is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). From \(4x\geq 28\), we get \(x\geq 7\). Hence the least integer solution is (7).
Step 3
Exam Tip
\(4x\geq 28\) से \(x\geq 7\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (7) है।
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असमानता \(2x-5\leq 9\) के हल में (x=7) क्यों शामिल है?
Why is (x=7) included in the solution of \(2x-5\leq 9\)?
#conceptual
#boundary included
#linear inequality
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A क्योंकि (x<7) / Because (x<7)
B क्योंकि (x>7) / Because (x>7)
C क्योंकि \(x\leq 7\) / Because \(x\leq 7\)
D क्योंकि \(x\geq 7\) / Because \(x\geq 7\)
Explanation opens after your attempt
Correct Answer
C. क्योंकि \(x\leq 7\) / Because \(x\leq 7\)
Step 1
Concept
The solution is \(x\leq 7\), so (x=7) is included. In \(\leq\), equality is also accepted.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(x\leq 7\) / Because \(x\leq 7\). The solution is \(x\leq 7\), so (x=7) is included. In \(\leq\), equality is also accepted.
Step 3
Exam Tip
हल \(x\leq 7\) है इसलिए (x=7) शामिल है। \(\leq\) में बराबरी भी स्वीकार होती है।
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असमानता (4x+1>17) के हल में सीमा बिंदु कौन सा है?
What is the boundary point in the solution of (4x+1>17)?
#boundary point
#strict inequality
#concept
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A (3)
B (5)
C (4)
D (17)
Explanation opens after your attempt
Step 1
Concept
From (4x>16), we get (x>4). Therefore the boundary point is (4), and it is not included.
Step 2
Why this answer is correct
The correct answer is C. (4). From (4x>16), we get (x>4). Therefore the boundary point is (4), and it is not included.
Step 3
Exam Tip
(4x>16) से (x>4) मिलता है। इसलिए सीमा बिंदु (4) है और यह शामिल नहीं है।
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असमानता \(7-2x\geq -9\) का हल अंतराल रूप में क्या है?
What is the interval form of the solution of \(7-2x\geq -9\)?
#interval notation
#negative coefficient
#closed endpoint
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A \([8,\infty\))
B (\(-\infty,8\))
C (\(8,\infty\))
D (\(-\infty,8]\)
Explanation opens after your attempt
Correct Answer
D. (\(-\infty,8]\)
Step 1
Concept
From \(-2x\geq -16\), we get \(x\leq 8\). Since equality is included, (8) gets a closed bracket.
Step 2
Why this answer is correct
The correct answer is D. (\(-\infty,8]\). From \(-2x\geq -16\), we get \(x\leq 8\). Since equality is included, (8) gets a closed bracket.
Step 3
Exam Tip
\(-2x\geq -16\) से \(x\leq 8\) मिलता है। बराबरी शामिल होने से (8) पर बंद कोष्ठक लगेगा।
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असमानता (2(4x-3)<5x+15) का हल क्या है?
What is the solution of (2(4x-3)<5x+15)?
#expansion
#variables both sides
#strict
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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 (8x-6<5x+15), we get (3x<21). Therefore (x<7).
Step 2
Why this answer is correct
The correct answer is A. (x<7). From (8x-6<5x+15), we get (3x<21). Therefore (x<7).
Step 3
Exam Tip
(8x-6<5x+15) से (3x<21) मिलता है। इसलिए (x<7) है।
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असमानता (6-(x+2)\leq 2x-5) को हल कीजिए।
Solve the inequality (6-(x+2)\leq 2x-5).
#minus bracket
#linear inequality
#solution
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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
B. \(x\geq 3\)
Step 1
Concept
Simplifying gives \(4-x\leq 2x-5\). Thus \(9\leq 3x\) and \(x\geq 3\).
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 3\). Simplifying gives \(4-x\leq 2x-5\). Thus \(9\leq 3x\) and \(x\geq 3\).
Step 3
Exam Tip
सरल करने पर \(4-x\leq 2x-5\) मिलता है। इसलिए \(9\leq 3x\) और \(x\geq 3\) है।
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असमानता \(\frac{2x+1}{3}\leq \frac{x+9}{6}\) का हल क्या है?
What is the solution of \(\frac{2x+1}{3}\leq \frac{x+9}{6}\)?
#fractional inequality
#lcm
#careful calculation
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A \(x\leq 7\)
B \(x\geq 7\)
C (x<7)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 7\)
Step 1
Concept
Multiplying by (6) gives \(4x+2\leq x+9\). So \(3x\leq 7\) and \(x\leq \frac{7}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 7\). Multiplying by (6) gives \(4x+2\leq x+9\). So \(3x\leq 7\) and \(x\leq \frac{7}{3}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(4x+2\leq x+9\) मिलता है। इसलिए \(3x\leq 7\) और \(x\leq \frac{7}{3}\) है।
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असमानता \(\frac{2x+1}{3}\leq \frac{x+9}{6}\) का सही हल कौन सा है?
Which is the correct solution of \(\frac{2x+1}{3}\leq \frac{x+9}{6}\)?
#fractional inequality
#lcm
#correct solution
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A \(x\leq \frac{7}{3}\)
B \(x\geq \frac{7}{3}\)
C \(x<\frac{7}{3}\)
D \(x>\frac{7}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{7}{3}\)
Step 1
Concept
Multiplying by (6) gives \(4x+2\leq x+9\). Therefore \(3x\leq 7\) and \(x\leq \frac{7}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{7}{3}\). Multiplying by (6) gives \(4x+2\leq x+9\). Therefore \(3x\leq 7\) and \(x\leq \frac{7}{3}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(4x+2\leq x+9\) मिलता है। इसलिए \(3x\leq 7\) और \(x\leq \frac{7}{3}\) है।
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यदि (2x+3) का मान (15) से अधिक है, तो (x) के लिए सही शर्त क्या है?
If the value of (2x+3) is greater than (15), what is the correct condition for (x)?
#word problem
#greater than
#linear inequality
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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+3>15), we get (2x>12). Therefore (x>6).
Step 2
Why this answer is correct
The correct answer is A. (x>6). From (2x+3>15), we get (2x>12). Therefore (x>6).
Step 3
Exam Tip
(2x+3>15) से (2x>12) मिलता है। इसलिए (x>6) है।
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असमानता \(3\leq \frac{x+2}{5}\leq 6\) का हल क्या है?
What is the solution of \(3\leq \frac{x+2}{5}\leq 6\)?
#compound inequality
#fraction
#closed interval
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A \(13\leq x\leq 28\)
B \(15\leq x\leq 30\)
C \(17\leq x\leq 32\)
D \(11\leq x\leq 26\)
Explanation opens after your attempt
Correct Answer
A. \(13\leq x\leq 28\)
Step 1
Concept
Multiplying by (5) gives \(15\leq x+2\leq 30\). Subtracting (2) gives \(13\leq x\leq 28\).
Step 2
Why this answer is correct
The correct answer is A. \(13\leq x\leq 28\). Multiplying by (5) gives \(15\leq x+2\leq 30\). Subtracting (2) gives \(13\leq x\leq 28\).
Step 3
Exam Tip
(5) से गुणा करने पर \(15\leq x+2\leq 30\) मिलता है। फिर (2) घटाने पर \(13\leq x\leq 28\) मिलता है।
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असमानता (2x-3>7) और (x<8) दोनों को संतुष्ट करने वाला अंतराल कौन सा है?
Which interval satisfies both (2x-3>7) and (x<8)?
#compound condition
#intersection
#interval
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A ((5,8))
B ([5,8))
C ((5,8])
D ([5,8])
Explanation opens after your attempt
Correct Answer
A. ((5,8))
Step 1
Concept
The first inequality gives (x>5), and the second is (x<8). Combining both gives (5<x<8).
Step 2
Why this answer is correct
The correct answer is A. ((5,8)). The first inequality gives (x>5), and the second is (x<8). Combining both gives (5<x<8).
Step 3
Exam Tip
पहली असमानता से (x>5) मिलता है और दूसरी (x<8) है। दोनों को मिलाकर (5<x<8) मिलता है।
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असमानता (3(5-x)+2<4x-11) का हल क्या है?
What is the solution of (3(5-x)+2<4x-11)?
#linear inequalities
#brackets
#variables both sides
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A (x<4)
B \(x\leq 4\)
C (x>4)
D \(x\geq 4\)
Explanation opens after your attempt
Step 1
Concept
Simplifying gives (17-3x<4x-11). Therefore (28<7x) and (x>4).
Step 2
Why this answer is correct
The correct answer is C. (x>4). Simplifying gives (17-3x<4x-11). Therefore (28<7x) and (x>4).
Step 3
Exam Tip
सरल करने पर (17-3x<4x-11) मिलता है। इसलिए (28<7x) और (x>4) है।
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असमानता \(\frac{x-4}{5}-\frac{x+1}{10}\geq 2\) का सही हल कौन सा है?
Which is the correct solution of \(\frac{x-4}{5}-\frac{x+1}{10}\geq 2\)?
#fractional inequality
#lcm
#algebraic solution
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A \(x\leq 29\)
B \(x\geq 29\)
C (x>29)
D (x<29)
Explanation opens after your attempt
Correct Answer
B. \(x\geq 29\)
Step 1
Concept
Multiplying by (10) gives \(2x-8-x-1\geq 20\). So \(x-9\geq 20\) and \(x\geq 29\).
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 29\). Multiplying by (10) gives \(2x-8-x-1\geq 20\). So \(x-9\geq 20\) and \(x\geq 29\).
Step 3
Exam Tip
(10) से गुणा करने पर \(2x-8-x-1\geq 20\) मिलता है। इसलिए \(x-9\geq 20\) और \(x\geq 29\) है।
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असमानता \(-2\leq \frac{3x+1}{4}<7\) का हल क्या है?
What is the solution of \(-2\leq \frac{3x+1}{4}<7\)?
#compound inequality
#fraction
#interval notation
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A \(-3<x\leq 9\)
B \(-3\leq x\leq 9\)
C \(-3\leq x<9\)
D (-3<x<9)
Explanation opens after your attempt
Correct Answer
C. \(-3\leq x<9\)
Step 1
Concept
Multiplying by (4) gives \(-8\leq 3x+1<28\). Subtracting (1) and dividing by (3) gives \(-3\leq x<9\).
Step 2
Why this answer is correct
The correct answer is C. \(-3\leq x<9\). Multiplying by (4) gives \(-8\leq 3x+1<28\). Subtracting (1) and dividing by (3) gives \(-3\leq x<9\).
Step 3
Exam Tip
(4) से गुणा करने पर \(-8\leq 3x+1<28\) मिलता है। फिर (1) घटाकर और (3) से भाग देकर \(-3\leq x<9\) मिलता है।
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एक छात्र को पास होने के लिए कम से कम (60) अंक चाहिए। यदि हर सही उत्तर पर (4) अंक मिलते हैं और सही उत्तरों की संख्या (x) है, तो न्यूनतम (x) क्या होगा?
A student needs at least (60) marks to pass. If each correct answer gives (4) marks and the number of correct answers is (x), what is the minimum (x)?
#word problem
#minimum value
#linear inequality
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A (12)
B (14)
C (16)
D (15)
Explanation opens after your attempt
Step 1
Concept
The condition is \(4x\geq 60\). Therefore \(x\geq 15\) and the minimum number of correct answers is (15).
Step 2
Why this answer is correct
The correct answer is D. (15). The condition is \(4x\geq 60\). Therefore \(x\geq 15\) and the minimum number of correct answers is (15).
Step 3
Exam Tip
शर्त \(4x\geq 60\) है। इसलिए \(x\geq 15\) और न्यूनतम सही उत्तर (15) हैं।
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