असमानता \( \frac{3x-5}{4}-\frac{x+1}{3}\leq 2 \) का हल कौन-सा है?
Which is the solution of the inequality \( \frac{3x-5}{4}-\frac{x+1}{3}\leq 2 \)?
#linear inequalities
#fractions
#expert
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A \(x\leq \frac{31}{5}\)
B \(x\geq \frac{31}{5}\)
C \(x<\frac{31}{5}\)
D \(x\leq -\frac{31}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{31}{5}\)
Step 1
Concept
Multiplying every term by (12) gives \(5x-31\leq 0\). In exams keep the inequality sign unchanged when multiplying by a positive number.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{31}{5}\). Multiplying every term by (12) gives \(5x-31\leq 0\). In exams keep the inequality sign unchanged when multiplying by a positive number.
Step 3
Exam Tip
हर पद को (12) से गुणा करने पर \(5x-31\leq 0\) मिलता है। परीक्षा में हरात्मक हटाते समय चिह्न ध्यान से रखें।
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असमानता \( \frac{3x-2}{5}-\frac{x+4}{2}\geq -1 \) का हल कौन-सा है?
Which is the solution of the inequality \( \frac{3x-2}{5}-\frac{x+4}{2}\geq -1 \)?
#linear inequalities
#fraction inequality
#expert
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A \(x\leq 14\)
B \(x\geq 14\)
C (x>14)
D \(x\leq -14\)
Explanation opens after your attempt
Correct Answer
B. \(x\geq 14\)
Step 1
Concept
Multiplying by (10) gives \(6x-4-5x-20\geq -10\). Therefore \(x\geq 14\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(x\geq 14\). Multiplying by (10) gives \(6x-4-5x-20\geq -10\). Therefore \(x\geq 14\) is correct.
Step 3
Exam Tip
(10) से गुणा करने पर \(6x-4-5x-20\geq -10\) मिलता है। इसलिए \(x\geq 14\) सही है।
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यदि ( -2(3x-4)>5-x ) हो तो (x) का हल-समुच्चय क्या है?
If ( -2(3x-4)>5-x ), what is the solution set of (x)?
#negative multiplication
#sign change
#linear inequalities
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A \(x<\frac{3}{5}\)
B \(x>\frac{3}{5}\)
C \(x<-\frac{3}{5}\)
D \(x>\frac{13}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x<\frac{3}{5}\)
Step 1
Concept
Simplification gives (-5x>-3) and division by a negative reverses the sign. This is the most common exam error.
Step 2
Why this answer is correct
The correct answer is A. \(x<\frac{3}{5}\). Simplification gives (-5x>-3) and division by a negative reverses the sign. This is the most common exam error.
Step 3
Exam Tip
सरलीकरण से (-5x>-3) मिलता है और ऋणात्मक से भाग देने पर चिह्न बदलता है। परीक्षा में इसी स्टेप पर सबसे अधिक गलती होती है।
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दोहरी असमानता \( -2<\frac{5-3x}{4}\leq 1 \) का सही हल-अंतराल क्या है?
What is the correct solution interval of the double inequality \( -2<\frac{5-3x}{4}\leq 1 \)?
#compound inequality
#negative division
#interval
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A \( \frac{1}{3}<x\leq \frac{13}{3} \)
B \( \frac{1}{3}\leq x\leq \frac{13}{3} \)
C \( \frac{1}{3}\leq x<\frac{13}{3} \)
D \( x<\frac{1}{3} \) या \(x\geq \frac{13}{3}\) / \(x<\frac{1}{3}\) or \(x\geq \frac{13}{3}\)
Explanation opens after your attempt
Correct Answer
C. \( \frac{1}{3}\leq x<\frac{13}{3} \)
Step 1
Concept
Dividing by (-3) reverses both inequality signs. Hence the solution is \( \frac{1}{3}\leq x<\frac{13}{3} \).
Step 2
Why this answer is correct
The correct answer is C. \( \frac{1}{3}\leq x<\frac{13}{3} \). Dividing by (-3) reverses both inequality signs. Hence the solution is \( \frac{1}{3}\leq x<\frac{13}{3} \).
Step 3
Exam Tip
(-3) से भाग देने पर दोनों असमानता-चिह्न उलटते हैं। इसलिए हल \( \frac{1}{3}\leq x<\frac{13}{3} \) है।
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यदि ( ax+7<1 ) का हल (x>3) है, तो (a) का मान क्या होगा?
If the solution of ( ax+7<1 ) is (x>3), what is the value of (a)?
#parameter inequality
#sign reversal
#expert
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A (2)
B (3)
C (-3)
D (-2)
Explanation opens after your attempt
Step 1
Concept
From (ax<-6), (x>3) occurs only when (a) is negative. Using \(\frac{-6}{a}=3\), we get (a=-2).
Step 2
Why this answer is correct
The correct answer is D. (-2). From (ax<-6), (x>3) occurs only when (a) is negative. Using \(\frac{-6}{a}=3\), we get (a=-2).
Step 3
Exam Tip
(ax<-6) से (x>3) तभी मिलेगा जब (a) ऋणात्मक हो। \(\frac{-6}{a}=3\) से (a=-2) मिलता है।
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दोहरी असमानता \( -3\leq 2x+5<11 \) का हल कौन-सा है?
Which is the solution of the double inequality \( -3\leq 2x+5<11 \)?
#compound inequality
#interval
#expert
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A \( -4\leq x<3 \)
B \( -1\leq x<8 \)
C \( -4<x\leq 3 \)
D \( x\leq -4 \) या (x>3) / \(x\leq -4\) or (x>3)
Explanation opens after your attempt
Correct Answer
A. \( -4\leq x<3 \)
Step 1
Concept
Subtract (5) from all parts and then divide by (2). Keep closed and open endpoints exactly as given.
Step 2
Why this answer is correct
The correct answer is A. \( -4\leq x<3 \). Subtract (5) from all parts and then divide by (2). Keep closed and open endpoints exactly as given.
Step 3
Exam Tip
सभी भागों से (5) घटाकर फिर (2) से भाग दें। बंद और खुले सिरों को वैसा ही रखें।
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यदि \(x\in \mathbb{Z}\), \( \frac{2x-7}{3}<5 \) और \( 4-\frac{x}{2}\leq 1 \), तो (x) के कितने पूर्णांक मान संभव हैं?
If \(x\in \mathbb{Z}\), \( \frac{2x-7}{3}<5 \), and \( 4-\frac{x}{2}\leq 1 \), how many integer values of (x) are possible?
#integer solution
#system inequalities
#expert
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The first inequality gives (x<11), and the second gives \(x\geq 6\). The integers are (6,7,8,9,10), so there are (5) values.
Step 2
Why this answer is correct
The correct answer is A. (5). The first inequality gives (x<11), and the second gives \(x\geq 6\). The integers are (6,7,8,9,10), so there are (5) values.
Step 3
Exam Tip
पहली असमानता से (x<11) और दूसरी से \(x\geq 6\) मिलता है। पूर्णांक (6,7,8,9,10) हैं, इसलिए कुल (5) मान हैं।
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यदि \( \frac{2x-3}{4}\geq \frac{x+5}{6} \), तो सबसे छोटा पूर्णांक (x) क्या होगा?
If \( \frac{2x-3}{4}\geq \frac{x+5}{6} \), what is the smallest integer (x)?
#integer solution
#fraction inequality
#expert
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (12) gives \(6x-9\geq 2x+10\) and \(x\geq \frac{19}{4}\). Therefore the smallest integer is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). Multiplying by (12) gives \(6x-9\geq 2x+10\) and \(x\geq \frac{19}{4}\). Therefore the smallest integer is (7).
Step 3
Exam Tip
(12) से गुणा करने पर \(6x-9\geq 2x+10\) और \(x\geq \frac{19}{4}\) मिलता है। इसलिए सबसे छोटा पूर्णांक (7) है।
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असमानता \( 4-\frac{3x+2}{5}>1+\frac{x-6}{2} \) का हल है:
The solution of \( 4-\frac{3x+2}{5}>1+\frac{x-6}{2} \) is:
#linear inequality
#simplification
#expert
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A \(x<\frac{29}{11}\)
B \(x>\frac{29}{11}\)
C \(x<-\frac{29}{11}\)
D \(x>\frac{11}{29}\)
Explanation opens after your attempt
Correct Answer
A. \(x<\frac{29}{11}\)
Step 1
Concept
Multiplying by (10) gives (40-6x-4>10+5x-30). Thus (66-11x>0) gives (x<6).
Step 2
Why this answer is correct
The correct answer is A. \(x<\frac{29}{11}\). Multiplying by (10) gives (40-6x-4>10+5x-30). Thus (66-11x>0) gives (x<6).
Step 3
Exam Tip
(10) से गुणा करने पर (40-6x-4>10+5x-30) मिलता है। अतः (66-11x>0) से (x<6) नहीं बल्कि \(x<\frac{66}{11}=6\) आता है।
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असमानता ( 5(2-x)\leq 3(4-x)-8 ) का हल-समुच्चय क्या है?
What is the solution set of ( 5(2-x)\leq 3(4-x)-8 )?
#brackets
#linear inequalities
#expert
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A \(x\geq 3\)
B \(x\leq 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 3\)
Step 1
Concept
Simplification gives \(10-5x\leq 4-3x\) and \(6\leq 2x\). Therefore \(x\geq 3\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 3\). Simplification gives \(10-5x\leq 4-3x\) and \(6\leq 2x\). Therefore \(x\geq 3\).
Step 3
Exam Tip
सरलीकरण से \(10-5x\leq 4-3x\) और \(6\leq 2x\) मिलता है। इसलिए \(x\geq 3\) है।
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यदि \( 7-2x\leq 3x+12<22-2x \), तो (x) का अंतराल क्या है?
If \( 7-2x\leq 3x+12<22-2x \), what is the interval of (x)?
#compound inequality
#interval notation
#expert
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A \(x\geq -1\) और (x<2) / \(x\geq -1\) and (x<2)
B (x>-1) और \(x\leq 2\) / (x>-1) and \(x\leq 2\)
C \(x\leq -1\) और (x>2) / \(x\leq -1\) and (x>2)
D (x<-1) या (x>2) / (x<-1) or (x>2)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -1\) और (x<2) / \(x\geq -1\) and (x<2)
Step 1
Concept
Solving both parts separately gives \(x\geq -1\) and (x<2). The combined solution is ([-1,2)).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -1\) और (x<2) / \(x\geq -1\) and (x<2). Solving both parts separately gives \(x\geq -1\) and (x<2). The combined solution is ([-1,2)).
Step 3
Exam Tip
दोनों भाग अलग-अलग हल करने पर \(x\geq -1\) और (x<2) मिलता है। संयुक्त हल ([-1,2)) है।
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असमानता \( \frac{5-2x}{3}\geq x-4 \) का हल है:
The solution of \( \frac{5-2x}{3}\geq x-4 \) is:
#linear inequality
#fractions
#expert
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A \(x\leq \frac{17}{5}\)
B \(x\geq \frac{17}{5}\)
C \(x<\frac{17}{5}\)
D \(x\leq -\frac{17}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{17}{5}\)
Step 1
Concept
Multiplying by (3) gives \(5-2x\geq 3x-12\). This gives \(17\geq 5x\), so \(x\leq \frac{17}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{17}{5}\). Multiplying by (3) gives \(5-2x\geq 3x-12\). This gives \(17\geq 5x\), so \(x\leq \frac{17}{5}\).
Step 3
Exam Tip
(3) से गुणा करने पर \(5-2x\geq 3x-12\) मिलता है। इससे \(17\geq 5x\) अर्थात \(x\leq \frac{17}{5}\) है।
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असमानता \( \frac{x+4}{2}-\frac{x-3}{5}<4 \) का हल कौन-सा है?
Which is the solution of \( \frac{x+4}{2}-\frac{x-3}{5}<4 \)?
#fraction simplification
#linear inequality
#expert
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A \(x<\frac{8}{3}\)
B \(x>\frac{8}{3}\)
C \(x<-\frac{8}{3}\)
D \(x>\frac{3}{8}\)
Explanation opens after your attempt
Correct Answer
A. \(x<\frac{8}{3}\)
Step 1
Concept
Multiplying by (10) gives (5x+20-2x+6<40). Therefore (3x<14), so \(x<\frac{14}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x<\frac{8}{3}\). Multiplying by (10) gives (5x+20-2x+6<40). Therefore (3x<14), so \(x<\frac{14}{3}\).
Step 3
Exam Tip
(10) से गुणा करने पर (5x+20-2x+6<40) मिलता है। इससे (3x<14) नहीं बल्कि (3x<14) के कारण \(x<\frac{14}{3}\) होगा।
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यदि ( 2(x-1)+3(x+2)\geq 4x+11 ), तो (x) के लिए सही कथन कौन-सा है?
If ( 2(x-1)+3(x+2)\geq 4x+11 ), which statement is correct for (x)?
#bracket expansion
#linear inequality
#expert
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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 left side is (5x+4). From \(5x+4\geq 4x+11\), we get \(x\geq 7\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 7\). The left side is (5x+4). From \(5x+4\geq 4x+11\), we get \(x\geq 7\).
Step 3
Exam Tip
बायाँ पक्ष (5x+4) है। \(5x+4\geq 4x+11\) से \(x\geq 7\) मिलता है।
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असमानता \( 0.4x-1.2\leq 0.1x+2.1 \) का हल है:
The solution of \( 0.4x-1.2\leq 0.1x+2.1 \) is:
#decimal inequality
#linear inequality
#expert
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A \(x\leq 11\)
B \(x\geq 11\)
C (x<11)
D \(x\leq -11\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 11\)
Step 1
Concept
Multiplying both sides by (10) gives \(4x-12\leq x+21\). Thus \(3x\leq 33\) and \(x\leq 11\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 11\). Multiplying both sides by (10) gives \(4x-12\leq x+21\). Thus \(3x\leq 33\) and \(x\leq 11\).
Step 3
Exam Tip
दोनों ओर (10) से गुणा करें तो \(4x-12\leq x+21\) मिलता है। इससे \(3x\leq 33\) और \(x\leq 11\) है।
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यदि \( \frac{2x+1}{3}-\frac{x-2}{4}\geq \frac{x+5}{6} \), तो हल क्या है?
If \( \frac{2x+1}{3}-\frac{x-2}{4}\geq \frac{x+5}{6} \), what is the solution?
#multi fraction
#linear inequality
#expert
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A \(x\geq -4\)
B \(x\leq -4\)
C (x>-4)
D \(x\leq 4\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -4\)
Step 1
Concept
Multiplying by (12) gives \(8x+4-3x+6\geq 2x+10\). Hence \(3x\geq 0\) and \(x\geq 0\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -4\). Multiplying by (12) gives \(8x+4-3x+6\geq 2x+10\). Hence \(3x\geq 0\) and \(x\geq 0\).
Step 3
Exam Tip
(12) से गुणा करने पर \(8x+4-3x+6\geq 2x+10\) मिलता है। इससे \(3x\geq 0\) और \(x\geq 0\) है।
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असमानता ( 9-4(x+1)<2x-7 ) को हल कीजिए।
Solve the inequality ( 9-4(x+1)<2x-7 ).
#expansion
#strict inequality
#expert
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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
Simplification gives (5-4x<2x-7) and (12<6x). Therefore (x>2).
Step 2
Why this answer is correct
The correct answer is A. (x>2). Simplification gives (5-4x<2x-7) and (12<6x). Therefore (x>2).
Step 3
Exam Tip
सरलीकरण से (5-4x<2x-7) और (12<6x) मिलता है। इसलिए (x>2) है।
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यदि \( \frac{3x-1}{2}\leq \frac{x+7}{3}<x+5 \), तो (x) का सही हल है:
If \( \frac{3x-1}{2}\leq \frac{x+7}{3}<x+5 \), the correct solution for (x) is:
#compound fractions
#interval
#expert
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A \(x\leq \frac{17}{7}\) और (x>-4) / \(x\leq \frac{17}{7}\) and (x>-4)
B \(x<\frac{17}{7}\) और \(x\geq -4\) / \(x<\frac{17}{7}\) and \(x\geq -4\)
C \(x\geq \frac{17}{7}\) और (x<-4) / \(x\geq \frac{17}{7}\) and (x<-4)
D \(x\leq -4\) या \(x>\frac{17}{7}\) / \(x\leq -4\) or \(x>\frac{17}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{17}{7}\) और (x>-4) / \(x\leq \frac{17}{7}\) and (x>-4)
Step 1
Concept
The first part gives \(x\leq \frac{17}{7}\) and the second gives (x>-4). Hence the combined solution is (\(-4,\frac{17}{7}]\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{17}{7}\) और (x>-4) / \(x\leq \frac{17}{7}\) and (x>-4). The first part gives \(x\leq \frac{17}{7}\) and the second gives (x>-4). Hence the combined solution is (\(-4,\frac{17}{7}]\).
Step 3
Exam Tip
पहले भाग से \(x\leq \frac{17}{7}\) और दूसरे से (x>-4) मिलता है। अतः संयुक्त हल (\(-4,\frac{17}{7}]\) है।
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असमानता ( -\frac{1}{2}(x-6)\leq \frac{3x+2}{4} ) का हल कौन-सा है?
Which is the solution of ( -\frac{1}{2}(x-6)\leq \frac{3x+2}{4} )?
#negative coefficient
#fraction inequality
#expert
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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
Multiplying by (4) gives \(-2x+12\leq 3x+2\). Thus \(10\leq 5x\) and \(x\geq 2\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 2\). Multiplying by (4) gives \(-2x+12\leq 3x+2\). Thus \(10\leq 5x\) and \(x\geq 2\).
Step 3
Exam Tip
(4) से गुणा करने पर \(-2x+12\leq 3x+2\) मिलता है। इससे \(10\leq 5x\) और \(x\geq 2\) है।
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यदि \(x\in \mathbb{N}\) और ( 2x-5<11 ), तो (x) के मानों की संख्या कितनी है?
If \(x\in \mathbb{N}\) and ( 2x-5<11 ), how many values of (x) are possible?
#natural numbers
#count
#linear inequality
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A (7)
B (8)
C (9)
D (6)
Explanation opens after your attempt
Step 1
Concept
The solution is (x<8), and natural values are from (1) to (7). Therefore there are (7) values.
Step 2
Why this answer is correct
The correct answer is A. (7). The solution is (x<8), and natural values are from (1) to (7). Therefore there are (7) values.
Step 3
Exam Tip
हल (x<8) है और प्राकृतिक मान (1) से (7) तक हैं। इसलिए कुल (7) मान हैं।
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असमानता \( 6-\frac{x}{3}\geq \frac{2x-1}{2} \) का हल है:
The solution of \( 6-\frac{x}{3}\geq \frac{2x-1}{2} \) is:
#fraction inequality
#exam practice
#expert
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A \(x\leq \frac{39}{8}\)
B \(x\geq \frac{39}{8}\)
C \(x<\frac{39}{8}\)
D \(x\leq -\frac{39}{8}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{39}{8}\)
Step 1
Concept
Multiplying by (6) gives \(36-2x\geq 6x-3\). Thus \(39\geq 8x\) and \(x\leq \frac{39}{8}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{39}{8}\). Multiplying by (6) gives \(36-2x\geq 6x-3\). Thus \(39\geq 8x\) and \(x\leq \frac{39}{8}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(36-2x\geq 6x-3\) मिलता है। इससे \(39\geq 8x\) और \(x\leq \frac{39}{8}\) है।
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यदि ( 3x+a<12 ) का हल (x<2) है, तो (a) का मान क्या है?
If the solution of ( 3x+a<12 ) is (x<2), what is the value of (a)?
#parameter inequality
#linear inequalities
#expert
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From the given solution \(\frac{12-a}{3}=2\). Therefore (12-a=6) and (a=6).
Step 2
Why this answer is correct
The correct answer is C. (6). From the given solution \(\frac{12-a}{3}=2\). Therefore (12-a=6) and (a=6).
Step 3
Exam Tip
दिए गए हल से \(\frac{12-a}{3}=2\) होगा। इसलिए (12-a=6) और (a=6) है।
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असमानता \( \frac{4x+3}{5}>2-\frac{x-1}{10} \) का हल कौन-सा है?
Which is the solution of \( \frac{4x+3}{5}>2-\frac{x-1}{10} \)?
#fraction inequality
#strict inequality
#expert
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A \(x>\frac{8}{3}\)
B \(x<\frac{8}{3}\)
C \(x>\frac{16}{9}\)
D \(x<\frac{16}{9}\)
Explanation opens after your attempt
Correct Answer
C. \(x>\frac{16}{9}\)
Step 1
Concept
Multiplying by (10) gives (8x+6>20-x+1). Thus (9x>15) and \(x>\frac{5}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(x>\frac{16}{9}\). Multiplying by (10) gives (8x+6>20-x+1). Thus (9x>15) and \(x>\frac{5}{3}\).
Step 3
Exam Tip
(10) से गुणा करने पर (8x+6>20-x+1) मिलता है। इससे (9x>15) और \(x>\frac{5}{3}\) है।
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यदि \( \frac{x-1}{2}+\frac{x-2}{3}\leq \frac{x+4}{6} \), तो (x) का हल क्या है?
If \( \frac{x-1}{2}+\frac{x-2}{3}\leq \frac{x+4}{6} \), what is the solution for (x)?
#multi fraction
#linear inequality
#expert
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A \(x\leq 3\)
B \(x\geq 3\)
C (x<3)
D \(x\leq \frac{7}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 3\)
Step 1
Concept
Multiplying by (6) gives \(3x-3+2x-4\leq x+4\). Hence \(4x\leq 11\) and \(x\leq \frac{11}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 3\). Multiplying by (6) gives \(3x-3+2x-4\leq x+4\). Hence \(4x\leq 11\) and \(x\leq \frac{11}{4}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(3x-3+2x-4\leq x+4\) मिलता है। इसलिए \(4x\leq 11\) और \(x\leq \frac{11}{4}\) है।
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असमानता ( 2(3-x)>x+9 ) का हल है:
The solution of ( 2(3-x)>x+9 ) is:
#brackets
#strict inequality
#expert
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A (x<-1)
B (x>-1)
C \(x\leq -1\)
D (x<1)
Explanation opens after your attempt
Step 1
Concept
Simplification gives (6-2x>x+9). Thus (-3>3x) and (x<-1).
Step 2
Why this answer is correct
The correct answer is A. (x<-1). Simplification gives (6-2x>x+9). Thus (-3>3x) and (x<-1).
Step 3
Exam Tip
सरलीकरण से (6-2x>x+9) मिलता है। इससे (-3>3x) और (x<-1) है।
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यदि \( \frac{7-3x}{4}<\frac{x+1}{2} \), तो सही हल कौन-सा है?
If \( \frac{7-3x}{4}<\frac{x+1}{2} \), which is the correct solution?
#fraction inequality
#sign analysis
#expert
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A (x>1)
B (x<1)
C \(x\geq 1\)
D (x>-1)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (4) gives (7-3x<2x+2). Thus (5<5x) and (x>1).
Step 2
Why this answer is correct
The correct answer is A. (x>1). Multiplying by (4) gives (7-3x<2x+2). Thus (5<5x) and (x>1).
Step 3
Exam Tip
(4) से गुणा करने पर (7-3x<2x+2) मिलता है। इससे (5<5x) और (x>1) है।
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असमानता \( -4\leq \frac{x-1}{3}<2 \) का हल कौन-सा अंतराल है?
Which interval is the solution of \( -4\leq \frac{x-1}{3}<2 \)?
#compound inequality
#interval
#expert
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A \(-11\leq x<7\)
B \(-12\leq x<6\)
C \(-13<x\leq 7\)
D \(-11<x\leq 7\)
Explanation opens after your attempt
Correct Answer
A. \(-11\leq x<7\)
Step 1
Concept
First multiply by (3), then add (1). Therefore \(-11\leq x<7\).
Step 2
Why this answer is correct
The correct answer is A. \(-11\leq x<7\). First multiply by (3), then add (1). Therefore \(-11\leq x<7\).
Step 3
Exam Tip
पहले (3) से गुणा करें और फिर (1) जोड़ें। इसलिए \(-11\leq x<7\) मिलता है।
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यदि \(x\in \mathbb{Z}\) और \( \frac{x+2}{3}\geq -1 \) तथा ( 2x-1<9 ), तो (x) के कितने पूर्णांक मान संभव हैं?
If \(x\in \mathbb{Z}\), \( \frac{x+2}{3}\geq -1 \), and ( 2x-1<9 ), how many integer values of (x) are possible?
#integer count
#system inequality
#expert
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The first inequality gives \(x\geq -5\), and the second gives (x<5). Integers from (-5) to (4) are (10) in total.
Step 2
Why this answer is correct
The correct answer is B. (8). The first inequality gives \(x\geq -5\), and the second gives (x<5). Integers from (-5) to (4) are (10) in total.
Step 3
Exam Tip
पहली असमानता से \(x\geq -5\) और दूसरी से (x<5) मिलता है। पूर्णांक (-5) से (4) तक कुल (10) हैं।
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असमानता \( 3-\frac{2x-5}{7}\leq \frac{x+4}{2} \) को हल कीजिए।
Solve the inequality \( 3-\frac{2x-5}{7}\leq \frac{x+4}{2} \).
#fraction inequality
#algebraic solution
#expert
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A \(x\geq \frac{13}{11}\)
B \(x\leq \frac{13}{11}\)
C \(x>\frac{13}{11}\)
D \(x\geq -\frac{13}{11}\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq \frac{13}{11}\)
Step 1
Concept
Multiplying by (14) gives \(42-4x+10\leq 7x+28\). Thus \(24\leq 11x\) and \(x\geq \frac{24}{11}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq \frac{13}{11}\). Multiplying by (14) gives \(42-4x+10\leq 7x+28\). Thus \(24\leq 11x\) and \(x\geq \frac{24}{11}\).
Step 3
Exam Tip
(14) से गुणा करने पर \(42-4x+10\leq 7x+28\) मिलता है। इससे \(24\leq 11x\) और \(x\geq \frac{24}{11}\) है।
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यदि \( kx-3\leq 9 \) का हल \(x\leq 4\) है और (k>0), तो (k) क्या है?
If the solution of \( kx-3\leq 9 \) is \(x\leq 4\) and (k>0), what is (k)?
#parameter
#linear inequality
#expert
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The solution is \(x\leq \frac{12}{k}\). Matching it with \(x\leq 4\) gives (k=3).
Step 2
Why this answer is correct
The correct answer is B. (3). The solution is \(x\leq \frac{12}{k}\). Matching it with \(x\leq 4\) gives (k=3).
Step 3
Exam Tip
हल \(x\leq \frac{12}{k}\) होगा। इसे \(x\leq 4\) से मिलाने पर (k=3) मिलता है।
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असमानता \( \frac{1-2x}{5}\leq \frac{3-x}{2} \) का हल है:
The solution of \( \frac{1-2x}{5}\leq \frac{3-x}{2} \) is:
#fraction inequality
#sign care
#expert
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A \(x\geq -\frac{13}{3}\)
B \(x\leq -\frac{13}{3}\)
C \(x\geq \frac{13}{3}\)
D \(x<-\frac{13}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -\frac{13}{3}\)
Step 1
Concept
Multiplying by (10) gives \(2-4x\leq 15-5x\). This gives \(x\leq 13\), not \(x\geq 13\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -\frac{13}{3}\). Multiplying by (10) gives \(2-4x\leq 15-5x\). This gives \(x\leq 13\), not \(x\geq 13\).
Step 3
Exam Tip
(10) से गुणा करने पर \(2-4x\leq 15-5x\) मिलता है। इससे \(x\leq 13\) नहीं बल्कि \(x\leq 13\) आता है।
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यदि \( 4x-7\leq 2x+1 \) और \(x\in \mathbb{N}\), तो सबसे बड़ा (x) क्या है?
If \( 4x-7\leq 2x+1 \) and \(x\in \mathbb{N}\), what is the greatest (x)?
#natural solution
#greatest integer
#expert
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The solution is \(2x\leq 8\), so \(x\leq 4\). The greatest natural number is (4).
Step 2
Why this answer is correct
The correct answer is C. (4). The solution is \(2x\leq 8\), so \(x\leq 4\). The greatest natural number is (4).
Step 3
Exam Tip
हल \(2x\leq 8\) से \(x\leq 4\) है। प्राकृतिक संख्याओं में सबसे बड़ा मान (4) है।
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असमानता ( 5x-2(3x-4)\geq 11 ) का हल क्या है?
What is the solution of ( 5x-2(3x-4)\geq 11 )?
#negative division
#linear inequality
#expert
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A \(x\leq -3\)
B \(x\geq -3\)
C (x<-3)
D \(x\leq 3\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq -3\)
Step 1
Concept
Simplification gives \(5x-6x+8\geq 11\) and \(-x\geq 3\). Therefore \(x\leq -3\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq -3\). Simplification gives \(5x-6x+8\geq 11\) and \(-x\geq 3\). Therefore \(x\leq -3\).
Step 3
Exam Tip
सरलीकरण से \(5x-6x+8\geq 11\) और \(-x\geq 3\) मिलता है। इसलिए \(x\leq -3\) है।
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यदि \( \frac{x}{2}+3>\frac{2x-1}{5} \), तो हल-समुच्चय क्या है?
If \( \frac{x}{2}+3>\frac{2x-1}{5} \), what is the solution set?
#fraction inequality
#solution set
#expert
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A (x>-32)
B (x<32)
C (x>-32)
D (x< -32)
Explanation opens after your attempt
Correct Answer
A. (x>-32)
Step 1
Concept
Multiplying by (10) gives (5x+30>4x-2). Hence (x>-32).
Step 2
Why this answer is correct
The correct answer is A. (x>-32). Multiplying by (10) gives (5x+30>4x-2). Hence (x>-32).
Step 3
Exam Tip
(10) से गुणा करने पर (5x+30>4x-2) मिलता है। इसलिए (x>-32) है।
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यदि \( \frac{3x+2}{8}<\frac{x-1}{2}+1 \), तो सही हल चुनिए।
If \( \frac{3x+2}{8}<\frac{x-1}{2}+1 \), choose the correct solution.
#fraction inequality
#expert
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A (x>-2)
B (x<-2)
C \(x\geq -2\)
D (x>2)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (8) gives (3x+2<4x-4+8). Hence (x>-2).
Step 2
Why this answer is correct
The correct answer is A. (x>-2). Multiplying by (8) gives (3x+2<4x-4+8). Hence (x>-2).
Step 3
Exam Tip
(8) से गुणा करने पर (3x+2<4x-4+8) मिलता है। इससे (x>-2) है।
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असमानता ( 12-3(2x+1)\leq x-5 ) का हल कौन-सा है?
Which is the solution of ( 12-3(2x+1)\leq x-5 )?
#brackets
#linear inequalities
#expert
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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
Simplification gives \(9-6x\leq x-5\). Therefore \(14\leq 7x\) and \(x\geq 2\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 2\). Simplification gives \(9-6x\leq x-5\). Therefore \(14\leq 7x\) and \(x\geq 2\).
Step 3
Exam Tip
सरलीकरण से \(9-6x\leq x-5\) मिलता है। इसलिए \(14\leq 7x\) और \(x\geq 2\) है।
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यदि \( \frac{x-6}{-3}>2 \), तो (x) के लिए सही हल है:
If \( \frac{x-6}{-3}>2 \), the correct solution for (x) is:
#negative denominator
#sign reversal
#expert
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A (x<0)
B (x>0)
C (x<-12)
D (x>12)
Explanation opens after your attempt
Step 1
Concept
Multiplying by negative (-3) reverses the sign. Hence (x-6<-6) and (x<0).
Step 2
Why this answer is correct
The correct answer is A. (x<0). Multiplying by negative (-3) reverses the sign. Hence (x-6<-6) and (x<0).
Step 3
Exam Tip
ऋणात्मक (-3) से गुणा करने पर चिह्न बदलता है। इसलिए (x-6<-6) और (x<0) है।
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असमानता \( \frac{2x+5}{3}\leq 7-\frac{x}{6} \) का हल-समुच्चय क्या है?
What is the solution set of \( \frac{2x+5}{3}\leq 7-\frac{x}{6} \)?
#fraction inequality
#linear solution
#expert
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A \(x\leq \frac{37}{5}\)
B \(x\geq \frac{37}{5}\)
C \(x<\frac{37}{5}\)
D \(x\leq -\frac{37}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{37}{5}\)
Step 1
Concept
Multiplying by (6) gives \(4x+10\leq 42-x\). Thus \(5x\leq 32\) and \(x\leq \frac{32}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{37}{5}\). Multiplying by (6) gives \(4x+10\leq 42-x\). Thus \(5x\leq 32\) and \(x\leq \frac{32}{5}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(4x+10\leq 42-x\) मिलता है। इससे \(5x\leq 32\) और \(x\leq \frac{32}{5}\) है।
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यदि ( 2x-3<5 ) और \( x+4\geq 1 \), तो संयुक्त हल क्या है?
If ( 2x-3<5 ) and \( x+4\geq 1 \), what is the combined solution?
#system of inequalities
#interval
#expert
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A \(-3\leq x<4\)
B \(-3<x\leq 4\)
C (x<-3) या \(x\geq 4\) / (x<-3) or \(x\geq 4\)
D \(-4\leq x<3\)
Explanation opens after your attempt
Correct Answer
A. \(-3\leq x<4\)
Step 1
Concept
The first inequality gives (x<4), and the second gives \(x\geq -3\). The combined solution is ([-3,4)).
Step 2
Why this answer is correct
The correct answer is A. \(-3\leq x<4\). The first inequality gives (x<4), and the second gives \(x\geq -3\). The combined solution is ([-3,4)).
Step 3
Exam Tip
पहली असमानता से (x<4) और दूसरी से \(x\geq -3\) मिलता है। संयुक्त हल ([-3,4)) है।
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असमानता ( 3(2x-1)-4(x+2)>x-9 ) का हल है:
The solution of ( 3(2x-1)-4(x+2)>x-9 ) is:
#expansion
#linear inequality
#expert
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A (x>2)
B (x<2)
C \(x\geq 2\)
D (x>-2)
Explanation opens after your attempt
Step 1
Concept
Simplification gives (6x-3-4x-8>x-9). Hence (x>2).
Step 2
Why this answer is correct
The correct answer is A. (x>2). Simplification gives (6x-3-4x-8>x-9). Hence (x>2).
Step 3
Exam Tip
सरलीकरण से (6x-3-4x-8>x-9) मिलता है। इससे (x>2) है।
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यदि \( \frac{5x-4}{6}\geq \frac{x+2}{3}+1 \), तो (x) का हल क्या है?
If \( \frac{5x-4}{6}\geq \frac{x+2}{3}+1 \), what is the solution for (x)?
#fraction inequality
#expert
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A \(x\geq 4\)
B \(x\leq 4\)
C (x>4)
D \(x\geq -4\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 4\)
Step 1
Concept
Multiplying by (6) gives \(5x-4\geq 2x+4+6\). Thus \(3x\geq 14\) and \(x\geq \frac{14}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 4\). Multiplying by (6) gives \(5x-4\geq 2x+4+6\). Thus \(3x\geq 14\) and \(x\geq \frac{14}{3}\).
Step 3
Exam Tip
(6) से गुणा करने पर \(5x-4\geq 2x+4+6\) मिलता है। अतः \(3x\geq 14\) और \(x\geq \frac{14}{3}\) है।
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यदि ( mx+2>8 ) का हल (x< -3) है, तो (m) का मान क्या है?
If the solution of ( mx+2>8 ) is (x< -3), what is the value of (m)?
#parameter
#negative coefficient
#expert
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A ( -2 )
B (2)
C (-3)
D (3)
Explanation opens after your attempt
Step 1
Concept
The solution is (mx>6), and (x<-3) requires (m) to be negative. From \(\frac{6}{m}=-3\), (m=-2).
Step 2
Why this answer is correct
The correct answer is A. ( -2 ). The solution is (mx>6), and (x<-3) requires (m) to be negative. From \(\frac{6}{m}=-3\), (m=-2).
Step 3
Exam Tip
हल (mx>6) है और (x<-3) तभी मिलेगा जब (m) ऋणात्मक हो। \(\frac{6}{m}=-3\) से (m=-2) है।
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असमानता \( \frac{x+1}{4}+\frac{x+3}{8}>1 \) को हल करें।
Solve the inequality \( \frac{x+1}{4}+\frac{x+3}{8}>1 \).
#fraction inequality
#algebra
#expert
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A \(x>\frac{1}{3}\)
B \(x<\frac{1}{3}\)
C \(x>\frac{4}{3}\)
D \(x<-\frac{1}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x>\frac{1}{3}\)
Step 1
Concept
Multiplying by (8) gives (2x+2+x+3>8). Thus (3x>3) and (x>1).
Step 2
Why this answer is correct
The correct answer is A. \(x>\frac{1}{3}\). Multiplying by (8) gives (2x+2+x+3>8). Thus (3x>3) and (x>1).
Step 3
Exam Tip
(8) से गुणा करने पर (2x+2+x+3>8) मिलता है। इससे (3x>3) और (x>1) है।
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यदि \(x\in \mathbb{Z}\) और \( -7\leq 2x-1<9 \), तो (x) के मानों का योग क्या है?
If \(x\in \mathbb{Z}\) and \( -7\leq 2x-1<9 \), what is the sum of values of (x)?
#integer sum
#compound inequality
#expert
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A (0)
B (1)
C (2)
D (3)
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Step 1
Concept
The solution is \(-3\leq x<5\). The sum of integers (-3,-2,-1,0,1,2,3,4) is (4).
Step 2
Why this answer is correct
The correct answer is A. (0). The solution is \(-3\leq x<5\). The sum of integers (-3,-2,-1,0,1,2,3,4) is (4).
Step 3
Exam Tip
हल \(-3\leq x<5\) है। पूर्णांक (-3,-2,-1,0,1,2,3,4) का योग (4) है।
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असमानता \( 2-\frac{3x-1}{4}<\frac{x+2}{3} \) का हल कौन-सा है?
Which is the solution of \( 2-\frac{3x-1}{4}<\frac{x+2}{3} \)?
#fraction inequality
#expert
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A \(x>\frac{14}{13}\)
B \(x<\frac{14}{13}\)
C \(x>\frac{7}{13}\)
D \(x<-\frac{14}{13}\)
Explanation opens after your attempt
Correct Answer
A. \(x>\frac{14}{13}\)
Step 1
Concept
Multiplying by (12) gives (24-9x+3<4x+8). Thus (19<13x) and \(x>\frac{19}{13}\).
Step 2
Why this answer is correct
The correct answer is A. \(x>\frac{14}{13}\). Multiplying by (12) gives (24-9x+3<4x+8). Thus (19<13x) and \(x>\frac{19}{13}\).
Step 3
Exam Tip
(12) से गुणा करने पर (24-9x+3<4x+8) मिलता है। इससे (19<13x) और \(x>\frac{19}{13}\) है।
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यदि \( 5-2x\geq -1 \) और ( 3x+4>1 ), तो संयुक्त हल है:
If \( 5-2x\geq -1 \) and ( 3x+4>1 ), the combined solution is:
#system inequality
#interval
#expert
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A \(-1<x\leq 3\)
B \(-1\leq x<3\)
C (x<-1) या (x>3) / (x<-1) or (x>3)
D \(-3<x\leq 1\)
Explanation opens after your attempt
Correct Answer
A. \(-1<x\leq 3\)
Step 1
Concept
The first gives \(x\leq 3\), and the second gives (x>-1). Therefore the combined solution is ((-1,3]).
Step 2
Why this answer is correct
The correct answer is A. \(-1<x\leq 3\). The first gives \(x\leq 3\), and the second gives (x>-1). Therefore the combined solution is ((-1,3]).
Step 3
Exam Tip
पहली से \(x\leq 3\) और दूसरी से (x>-1) मिलता है। इसलिए संयुक्त हल ((-1,3]) है।
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असमानता \( \frac{2-5x}{3}\geq 4x-7 \) का हल है:
The solution of \( \frac{2-5x}{3}\geq 4x-7 \) is:
#linear inequality
#fraction
#expert
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A \(x\leq \frac{23}{17}\)
B \(x\geq \frac{23}{17}\)
C \(x<\frac{23}{17}\)
D \(x\leq -\frac{23}{17}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{23}{17}\)
Step 1
Concept
Multiplying by (3) gives \(2-5x\geq 12x-21\). Thus \(23\geq 17x\) and \(x\leq \frac{23}{17}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{23}{17}\). Multiplying by (3) gives \(2-5x\geq 12x-21\). Thus \(23\geq 17x\) and \(x\leq \frac{23}{17}\).
Step 3
Exam Tip
(3) से गुणा करने पर \(2-5x\geq 12x-21\) मिलता है। इससे \(23\geq 17x\) और \(x\leq \frac{23}{17}\) है।
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यदि \( \frac{x-5}{2}\leq \frac{3-x}{4} \), तो (x) का हल क्या है?
If \( \frac{x-5}{2}\leq \frac{3-x}{4} \), what is the solution for (x)?
#fraction inequality
#expert
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A \(x\leq \frac{13}{3}\)
B \(x\geq \frac{13}{3}\)
C \(x<\frac{13}{3}\)
D \(x\leq -\frac{13}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq \frac{13}{3}\)
Step 1
Concept
Multiplying by (4) gives \(2x-10\leq 3-x\). Thus \(3x\leq 13\) and \(x\leq \frac{13}{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq \frac{13}{3}\). Multiplying by (4) gives \(2x-10\leq 3-x\). Thus \(3x\leq 13\) and \(x\leq \frac{13}{3}\).
Step 3
Exam Tip
(4) से गुणा करने पर \(2x-10\leq 3-x\) मिलता है। इससे \(3x\leq 13\) और \(x\leq \frac{13}{3}\) है।
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असमानता \( \frac{3}{2}x-4<\frac{1}{3}x+3 \) का हल कौन-सा है?
Which is the solution of \( \frac{3}{2}x-4<\frac{1}{3}x+3 \)?
#rational coefficients
#linear inequality
#expert
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A (x<6)
B (x>6)
C \(x\leq 6\)
D \(x<\frac{7}{6}\)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (6) gives (9x-24<2x+18). Thus (7x<42) and (x<6).
Step 2
Why this answer is correct
The correct answer is A. (x<6). Multiplying by (6) gives (9x-24<2x+18). Thus (7x<42) and (x<6).
Step 3
Exam Tip
(6) से गुणा करने पर (9x-24<2x+18) मिलता है। इससे (7x<42) और (x<6) है।
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यदि \( 2p-5\leq x< p+4 \) का हल-अंतराल खाली नहीं है, तो (p) पर क्या शर्त होगी?
If the solution interval \( 2p-5\leq x< p+4 \) is non-empty, what condition must (p) satisfy?
#parameter interval
#expert
#linear inequalities
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A (p<9)
B \(p\leq 9\)
C (p>9)
D \(p\geq 9\)
Explanation opens after your attempt
Step 1
Concept
For the interval to be non-empty, the left endpoint must be less than the right open endpoint. From (2p-5<p+4), (p<9).
Step 2
Why this answer is correct
The correct answer is A. (p<9). For the interval to be non-empty, the left endpoint must be less than the right open endpoint. From (2p-5<p+4), (p<9).
Step 3
Exam Tip
अंतराल खाली न हो इसके लिए बायाँ सिरा दाएँ खुले सिरे से छोटा होना चाहिए। (2p-5<p+4) से (p<9) मिलता है।
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