असमानता (x+8>20) का हल क्या है?
What is the solution of the inequality (x+8>20)?
#linear inequalities
#one variable
#subtraction
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A (x>12)
B (x<12)
C \(x\ge 12\)
D \(x\le 12\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (8) from both sides gives (x>12). Addition or subtraction does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>12). Subtracting (8) from both sides gives (x>12). Addition or subtraction does not change the sign.
Step 3
Exam Tip
दोनों पक्षों से (8) घटाने पर (x>12) मिलता है। जोड़ या घटाव में चिह्न नहीं बदलता।
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असमानता \(x-11\le 4\) का हल क्या है?
What is the solution of the inequality \(x-11\le 4\)?
#linear inequalities
#one variable
#addition
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A \(x\le 15\)
B \(x\ge 15\)
C (x<15)
D (x>15)
Explanation opens after your attempt
Correct Answer
A. \(x\le 15\)
Step 1
Concept
Adding (11) to both sides gives \(x\le 15\). Keep the equality part of the sign till the end.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 15\). Adding (11) to both sides gives \(x\le 15\). Keep the equality part of the sign till the end.
Step 3
Exam Tip
दोनों पक्षों में (11) जोड़ने पर \(x\le 15\) मिलता है। बराबरी वाला चिह्न अंत तक रखें।
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असमानता (6x<42) का हल क्या है?
What is the solution of the inequality (6x<42)?
#linear inequalities
#positive coefficient
#division
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A (x<7)
B (x>7)
C \(x\le 7\)
D \(x\ge 7\)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (6) gives (x<7). Dividing by a positive number keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x<7). Dividing both sides by (6) gives (x<7). Dividing by a positive number keeps the sign unchanged.
Step 3
Exam Tip
दोनों पक्षों को (6) से भाग देने पर (x<7) मिलता है। धनात्मक संख्या से भाग देने पर चिह्न वही रहता है।
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असमानता \(-3x\ge 21\) का हल क्या है?
What is the solution of the inequality \(-3x\ge 21\)?
#linear inequalities
#negative coefficient
#sign reversal
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A \(x\le -7\)
B \(x\ge -7\)
C (x<-7)
D (x>-7)
Explanation opens after your attempt
Correct Answer
A. \(x\le -7\)
Step 1
Concept
Dividing by (-3) reverses the sign and gives \(x\le -7\). Reverse the sign while dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\le -7\). Dividing by (-3) reverses the sign and gives \(x\le -7\). Reverse the sign while dividing by a negative number.
Step 3
Exam Tip
(-3) से भाग देने पर चिह्न पलटता है और \(x\le -7\) मिलता है। ऋणात्मक से भाग देते समय चिह्न बदलें।
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असमानता (4x+6>30) का हल क्या है?
What is the solution of the inequality (4x+6>30)?
#linear inequalities
#two step
#greater than
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A (x>6)
B (x<6)
C \(x\ge 6\)
D \(x\le 6\)
Explanation opens after your attempt
Step 1
Concept
First subtract (6) to get (4x>24), so (x>6). Remove the constant term first.
Step 2
Why this answer is correct
The correct answer is A. (x>6). First subtract (6) to get (4x>24), so (x>6). Remove the constant term first.
Step 3
Exam Tip
पहले (6) घटाने पर (4x>24), इसलिए (x>6)। स्थिर पद पहले हटाएं।
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असमानता \(9x-5\le 31\) का हल क्या है?
What is the solution of the inequality \(9x-5\le 31\)?
#linear inequalities
#two step
#less than equal
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A \(x\le 4\)
B \(x\ge 4\)
C (x<4)
D (x>4)
Explanation opens after your attempt
Correct Answer
A. \(x\le 4\)
Step 1
Concept
Adding (5) to both sides gives \(9x\le 36\), so \(x\le 4\). Division by a positive coefficient does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 4\). Adding (5) to both sides gives \(9x\le 36\), so \(x\le 4\). Division by a positive coefficient does not change the sign.
Step 3
Exam Tip
दोनों पक्षों में (5) जोड़ने पर \(9x\le 36\), इसलिए \(x\le 4\)। धनात्मक गुणांक से भाग देने पर चिह्न नहीं बदलता।
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असमानता (18-4x>2) का हल क्या है?
What is the solution of the inequality (18-4x>2)?
#linear inequalities
#negative variable
#sign reversal
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A (x<4)
B (x>4)
C \(x\le 4\)
D \(x\ge 4\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (18) gives (-4x>-16), then dividing by (-4) gives (x<4). The sign reverses in negative division.
Step 2
Why this answer is correct
The correct answer is A. (x<4). Subtracting (18) gives (-4x>-16), then dividing by (-4) gives (x<4). The sign reverses in negative division.
Step 3
Exam Tip
(18) घटाने पर (-4x>-16), फिर (-4) से भाग देने पर (x<4)। ऋणात्मक भाग पर चिह्न पलटता है।
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असमानता \(21-7x\le 0\) का हल क्या है?
What is the solution of the inequality \(21-7x\le 0\)?
#linear inequalities
#zero comparison
#negative coefficient
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A \(x\ge 3\)
B \(x\le 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
From \(21-7x\le 0\), we get \(-7x\le -21\), so \(x\ge 3\). The direction changes when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). From \(21-7x\le 0\), we get \(-7x\le -21\), so \(x\ge 3\). The direction changes when dividing by a negative number.
Step 3
Exam Tip
\(21-7x\le 0\) से \(-7x\le -21\), इसलिए \(x\ge 3\)। ऋणात्मक से भाग देने पर दिशा बदलती है।
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असमानता (3x+10<x+22) का हल क्या है?
What is the solution of the inequality (3x+10<x+22)?
#linear inequalities
#variables both sides
#simplification
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A (x<6)
B (x>6)
C \(x\le 6\)
D \(x\ge 6\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (x) from both sides gives (2x+10<22), so (x<6). Keep variable terms on one side.
Step 2
Why this answer is correct
The correct answer is A. (x<6). Subtracting (x) from both sides gives (2x+10<22), so (x<6). Keep variable terms on one side.
Step 3
Exam Tip
दोनों पक्षों से (x) घटाने पर (2x+10<22), इसलिए (x<6)। चर पदों को एक तरफ रखें।
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असमानता \(8x-3\ge 5x+18\) का हल क्या है?
What is the solution of the inequality \(8x-3\ge 5x+18\)?
#linear inequalities
#variables both sides
#greater equal
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A \(x\ge 7\)
B \(x\le 7\)
C (x>7)
D (x<7)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 7\)
Step 1
Concept
Subtracting (5x) and adding (3) gives \(3x\ge 21\), so \(x\ge 7\). Combine like terms carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 7\). Subtracting (5x) and adding (3) gives \(3x\ge 21\), so \(x\ge 7\). Combine like terms carefully.
Step 3
Exam Tip
(5x) घटाने और (3) जोड़ने पर \(3x\ge 21\), इसलिए \(x\ge 7\)। समान पदों को ध्यान से मिलाएं।
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असमानता (5(x+1)>25) का हल क्या है?
What is the solution of the inequality (5(x+1)>25)?
#linear inequalities
#brackets
#positive factor
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A (x>4)
B (x<4)
C \(x\ge 4\)
D \(x\le 4\)
Explanation opens after your attempt
Step 1
Concept
Dividing by (5) gives (x+1>5), so (x>4). A positive multiplier keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x>4). Dividing by (5) gives (x+1>5), so (x>4). A positive multiplier keeps the sign unchanged.
Step 3
Exam Tip
(5) से भाग देने पर (x+1>5), इसलिए (x>4)। धनात्मक गुणक से चिह्न वही रहता है।
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असमानता \(3(x-6)\le 12\) का हल क्या है?
What is the solution of the inequality \(3(x-6)\le 12\)?
#linear inequalities
#brackets
#less than equal
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A \(x\le 10\)
B \(x\ge 10\)
C (x<10)
D (x>10)
Explanation opens after your attempt
Correct Answer
A. \(x\le 10\)
Step 1
Concept
Dividing by (3) gives \(x-6\le 4\), so \(x\le 10\). In bracket questions, do the easy division first.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 10\). Dividing by (3) gives \(x-6\le 4\), so \(x\le 10\). In bracket questions, do the easy division first.
Step 3
Exam Tip
(3) से भाग देने पर \(x-6\le 4\), इसलिए \(x\le 10\)। कोष्ठक वाले प्रश्न में सरल भाग पहले करें।
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असमानता (7(x-2)<2x+13) का हल क्या है?
What is the solution of the inequality (7(x-2)<2x+13)?
#linear inequalities
#brackets
#fraction answer
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A \(x<\frac{27}{5}\)
B \(x>\frac{27}{5}\)
C \(x\le \frac{27}{5}\)
D \(x\ge \frac{27}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x<\frac{27}{5}\)
Step 1
Concept
Opening brackets gives (7x-14<2x+13), so (5x<27) and \(x<\frac{27}{5}\). A fractional answer can also be correct.
Step 2
Why this answer is correct
The correct answer is A. \(x<\frac{27}{5}\). Opening brackets gives (7x-14<2x+13), so (5x<27) and \(x<\frac{27}{5}\). A fractional answer can also be correct.
Step 3
Exam Tip
कोष्ठक खोलने पर (7x-14<2x+13), इसलिए (5x<27) और \(x<\frac{27}{5}\)। भिन्न उत्तर भी सही हल हो सकता है।
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असमानता \(4(x+3)\ge 2x+20\) का हल क्या है?
What is the solution of the inequality \(4(x+3)\ge 2x+20\)?
#linear inequalities
#brackets
#variables both sides
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A \(x\ge 4\)
B \(x\le 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
From \(4x+12\ge 2x+20\), we get \(2x\ge 8\), so \(x\ge 4\). Opening brackets correctly is important.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). From \(4x+12\ge 2x+20\), we get \(2x\ge 8\), so \(x\ge 4\). Opening brackets correctly is important.
Step 3
Exam Tip
\(4x+12\ge 2x+20\) से \(2x\ge 8\), इसलिए \(x\ge 4\)। कोष्ठक सही खोलना जरूरी है।
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असमानता \(\frac{x}{5}+3<9\) का हल क्या है?
What is the solution of the inequality \(\frac{x}{5}+3<9\)?
#linear inequalities
#fractions
#one variable
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A (x<30)
B (x>30)
C \(x\le 30\)
D \(x\ge 30\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (3) gives \(\frac{x}{5}<6\), so (x<30). Multiplying by a positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<30). Subtracting (3) gives \(\frac{x}{5}<6\), so (x<30). Multiplying by a positive denominator does not change the sign.
Step 3
Exam Tip
(3) घटाने पर \(\frac{x}{5}<6\), इसलिए (x<30)। धनात्मक हर से गुणा करने पर चिह्न नहीं बदलता।
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असमानता \(\frac{x+5}{2}\ge 8\) का हल क्या है?
What is the solution of the inequality \(\frac{x+5}{2}\ge 8\)?
#linear inequalities
#fractions
#greater equal
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A \(x\ge 11\)
B \(x\le 11\)
C (x>11)
D (x<11)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 11\)
Step 1
Concept
Multiplying by (2) gives \(x+5\ge 16\), so \(x\ge 11\). Remove the fraction first.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 11\). Multiplying by (2) gives \(x+5\ge 16\), so \(x\ge 11\). Remove the fraction first.
Step 3
Exam Tip
(2) से गुणा करने पर \(x+5\ge 16\), इसलिए \(x\ge 11\)। पहले भिन्न हटाएं।
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असमानता \(\frac{4x-1}{3}\le 5\) का हल क्या है?
What is the solution of the inequality \(\frac{4x-1}{3}\le 5\)?
#linear inequalities
#fractions
#two step
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A \(x\le 4\)
B \(x\ge 4\)
C (x<4)
D (x>4)
Explanation opens after your attempt
Correct Answer
A. \(x\le 4\)
Step 1
Concept
Multiplying by (3) gives \(4x-1\le 15\), so \(x\le 4\). A positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 4\). Multiplying by (3) gives \(4x-1\le 15\), so \(x\le 4\). A positive denominator does not change the sign.
Step 3
Exam Tip
(3) से गुणा करने पर \(4x-1\le 15\), इसलिए \(x\le 4\)। धनात्मक हर चिह्न नहीं बदलता।
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असमानता \(-\frac{x}{6}\ge 3\) का हल क्या है?
What is the solution of the inequality \(-\frac{x}{6}\ge 3\)?
#linear inequalities
#negative fraction
#sign reversal
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A \(x\le -18\)
B \(x\ge -18\)
C (x<-18)
D (x>-18)
Explanation opens after your attempt
Correct Answer
A. \(x\le -18\)
Step 1
Concept
Multiplying both sides by (-6) reverses the sign and gives \(x\le -18\). Change the direction in negative multiplication.
Step 2
Why this answer is correct
The correct answer is A. \(x\le -18\). Multiplying both sides by (-6) reverses the sign and gives \(x\le -18\). Change the direction in negative multiplication.
Step 3
Exam Tip
दोनों पक्षों को (-6) से गुणा करने पर चिह्न पलटता है और \(x\le -18\) मिलता है। ऋणात्मक गुणा में दिशा बदलें।
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असमानता \(\frac{2x+7}{4}>6\) का हल क्या है?
What is the solution of the inequality \(\frac{2x+7}{4}>6\)?
#linear inequalities
#fractions
#fraction answer
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A \(x>\frac{17}{2}\)
B \(x<\frac{17}{2}\)
C \(x\ge \frac{17}{2}\)
D \(x\le \frac{17}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x>\frac{17}{2}\)
Step 1
Concept
Multiplying by (4) gives (2x+7>24), so \(x>\frac{17}{2}\). A fractional form of the answer is acceptable.
Step 2
Why this answer is correct
The correct answer is A. \(x>\frac{17}{2}\). Multiplying by (4) gives (2x+7>24), so \(x>\frac{17}{2}\). A fractional form of the answer is acceptable.
Step 3
Exam Tip
(4) से गुणा करने पर (2x+7>24), इसलिए \(x>\frac{17}{2}\)। भिन्न रूप में उत्तर स्वीकार्य है।
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असमानता \(2x+5\ge 17\) का अंतराल रूप कौन सा है?
Which interval form represents the solution of \(2x+5\ge 17\)?
#linear inequalities
#interval notation
#closed endpoint
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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
The solution is \(x\ge 6\), so the interval is \([6,\infty\)). The sign \(\ge\) uses a closed bracket.
Step 2
Why this answer is correct
The correct answer is A. \([6,\infty\)). The solution is \(x\ge 6\), so the interval is \([6,\infty\)). The sign \(\ge\) uses a closed bracket.
Step 3
Exam Tip
हल \(x\ge 6\) है, इसलिए अंतराल \([6,\infty\)) होगा। \(\ge\) में बंद कोष्ठक लगता है।
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असमानता (5x-10<15) का अंतराल रूप कौन सा है?
Which interval form represents the solution of (5x-10<15)?
#linear inequalities
#interval notation
#open endpoint
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A (\(-\infty,5\))
B (\(-\infty,5]\)
C (\(5,\infty\))
D \([5,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,5\))
Step 1
Concept
The solution is (x<5), so the interval is (\(-\infty,5\)). Use an open bracket for a strict inequality.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,5\)). The solution is (x<5), so the interval is (\(-\infty,5\)). Use an open bracket for a strict inequality.
Step 3
Exam Tip
हल (x<5) है, इसलिए अंतराल (\(-\infty,5\)) होगा। सख्त असमानता में खुला कोष्ठक लगाएं।
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असमानता \(12\le x+9\) का हल क्या है?
What is the solution of the inequality \(12\le x+9\)?
#linear inequalities
#rewrite inequality
#greater equal
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A \(x\ge 3\)
B \(x\le 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
Subtracting (9) gives \(3\le x\), that is \(x\ge 3\). Writing the answer starting with (x) is clearer.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). Subtracting (9) gives \(3\le x\), that is \(x\ge 3\). Writing the answer starting with (x) is clearer.
Step 3
Exam Tip
(9) घटाने पर \(3\le x\), अर्थात \(x\ge 3\)। उत्तर को (x) से शुरू करके लिखना स्पष्ट रहता है।
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असमानता (30>5x) का हल क्या है?
What is the solution of the inequality (30>5x)?
#linear inequalities
#rewrite inequality
#less than
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A (x<6)
B (x>6)
C \(x\le 6\)
D \(x\ge 6\)
Explanation opens after your attempt
Step 1
Concept
Dividing by (5) gives (6>x), that is (x<6). Keep the direction correct when rewriting the inequality.
Step 2
Why this answer is correct
The correct answer is A. (x<6). Dividing by (5) gives (6>x), that is (x<6). Keep the direction correct when rewriting the inequality.
Step 3
Exam Tip
(5) से भाग देने पर (6>x), अर्थात (x<6)। असमानता को पलटकर लिखते समय दिशा सही रखें।
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कौन सा मान असमानता \(10-2x\ge 4\) को संतुष्ट नहीं करता?
Which value does not satisfy the inequality \(10-2x\ge 4\)?
#linear inequalities
#not satisfying
#negative coefficient
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A (x=4)
B (x=3)
C (x=2)
D (x=1)
Explanation opens after your attempt
Step 1
Concept
The solution is \(x\le 3\), so (x=4) does not satisfy it. Remember to reverse the sign with a negative coefficient.
Step 2
Why this answer is correct
The correct answer is A. (x=4). The solution is \(x\le 3\), so (x=4) does not satisfy it. Remember to reverse the sign with a negative coefficient.
Step 3
Exam Tip
हल \(x\le 3\) है, इसलिए (x=4) संतुष्ट नहीं करता। ऋणात्मक गुणांक पर चिह्न पलटना याद रखें।
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यदि (x) एक पूर्णांक है और (x+6<11), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (x+6<11), what is the greatest possible (x)?
#linear inequalities
#integer solution
#greatest integer
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A (4)
B (5)
C (6)
D (11)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x<5), so the greatest integer is (4). A strict sign does not include the boundary.
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives (x<5), so the greatest integer is (4). A strict sign does not include the boundary.
Step 3
Exam Tip
असमानता से (x<5) मिलता है, इसलिए सबसे बड़ा पूर्णांक (4) है। सख्त चिह्न में सीमा शामिल नहीं होती।
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यदि (x) एक पूर्णांक है और \(3x\ge 24\), तो सबसे छोटा संभव (x) क्या है?
If (x) is an integer and \(3x\ge 24\), what is the least possible (x)?
#linear inequalities
#integer solution
#least integer
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A (8)
B (7)
C (9)
D (24)
Explanation opens after your attempt
Step 1
Concept
Dividing by (3) gives \(x\ge 8\), so the least integer is (8). The sign \(\ge\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (8). Dividing by (3) gives \(x\ge 8\), so the least integer is (8). The sign \(\ge\) includes the boundary value.
Step 3
Exam Tip
(3) से भाग देने पर \(x\ge 8\), इसलिए सबसे छोटा पूर्णांक (8) है। \(\ge\) सीमा मान को शामिल करता है।
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यदि (x) एक प्राकृतिक संख्या है और \(x\le 6\), तो हल समुच्चय क्या है?
If (x) is a natural number and \(x\le 6\), what is the solution set?
#linear inequalities
#natural numbers
#solution set
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A ({1,2,3,4,5,6})
B ({0,1,2,3,4,5,6})
C ({1,2,3,4,5})
D ({6,7,8})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4,5,6})
Step 1
Concept
Natural numbers from (1) to (6) are included. Because of \(\le\), (6) is also included.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4,5,6}). Natural numbers from (1) to (6) are included. Because of \(\le\), (6) is also included.
Step 3
Exam Tip
प्राकृतिक संख्याओं में (1) से (6) तक के मान शामिल होंगे। \(\le\) के कारण (6) भी शामिल है।
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यदि (x) एक पूर्ण संख्या है और (x<4), तो हल समुच्चय क्या है?
If (x) is a whole number and (x<4), what is the solution set?
#linear inequalities
#whole numbers
#solution set
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A ({0,1,2,3})
B ({1,2,3,4})
C ({0,1,2,3,4})
D ({4,5,6})
Explanation opens after your attempt
Correct Answer
A. ({0,1,2,3})
Step 1
Concept
Whole numbers start from (0), and (4) is not included in (x<4). Therefore the solution is ({0,1,2,3}).
Step 2
Why this answer is correct
The correct answer is A. ({0,1,2,3}). Whole numbers start from (0), and (4) is not included in (x<4). Therefore the solution is ({0,1,2,3}).
Step 3
Exam Tip
पूर्ण संख्याएं (0) से शुरू होती हैं और (x<4) में (4) शामिल नहीं है। इसलिए हल ({0,1,2,3}) है।
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असमानता \(x+12\ge 25\) हल करते समय पहला सही कदम कौन सा है?
What is the correct first step while solving \(x+12\ge 25\)?
#linear inequalities
#first step
#operation
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A दोनों पक्षों से (12) घटाएं / Subtract (12) from both sides
B दोनों पक्षों में (12) जोड़ें / Add (12) to both sides
C दोनों पक्षों को (12) से गुणा करें / Multiply both sides by (12)
D दोनों पक्षों को (12) से भाग दें / Divide both sides by (12)
Explanation opens after your attempt
Correct Answer
A. दोनों पक्षों से (12) घटाएं / Subtract (12) from both sides
Step 1
Concept
Subtracting (12) is the correct first step to isolate (x). Choose the inverse operation.
Step 2
Why this answer is correct
The correct answer is A. दोनों पक्षों से (12) घटाएं / Subtract (12) from both sides. Subtracting (12) is the correct first step to isolate (x). Choose the inverse operation.
Step 3
Exam Tip
(x) को अलग करने के लिए (12) घटाना सही पहला कदम है। उल्टा ऑपरेशन चुनें।
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असमानता (2x-3<9) में (x=6) रखने पर कथन कैसा होगा?
What happens when (x=6) is put in (2x-3<9)?
#linear inequalities
#checking solution
#strict inequality
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A कथन गलत होगा / The statement will be false
B कथन सही होगा / The statement will be true
C हल (x<6) नहीं होगा / The solution will not be (x<6)
D चिह्न (>) बन जाएगा / The sign becomes (>)
Explanation opens after your attempt
Correct Answer
A. कथन गलत होगा / The statement will be false
Step 1
Concept
Putting (x=6) gives (12-3<9), that is (9<9), which is false. Equality is not allowed in a strict inequality.
Step 2
Why this answer is correct
The correct answer is A. कथन गलत होगा / The statement will be false. Putting (x=6) gives (12-3<9), that is (9<9), which is false. Equality is not allowed in a strict inequality.
Step 3
Exam Tip
(x=6) रखने पर (12-3<9) यानी (9<9) गलत है। सख्त असमानता में बराबरी मान्य नहीं होती।
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असमानता \(6x+4\le 40\) में (x=6) रखने पर क्या होगा?
What happens when (x=6) is put in \(6x+4\le 40\)?
#linear inequalities
#checking solution
#equality included
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A कथन सही होगा / The statement will be true
B कथन गलत होगा / The statement will be false
C हल केवल (x<6) होगा / The solution will only be (x<6)
D चिह्न (<) बन जाएगा / The sign becomes (<)
Explanation opens after your attempt
Correct Answer
A. कथन सही होगा / The statement will be true
Step 1
Concept
Putting (x=6) gives \(36+4\le 40\), that is \(40\le 40\), which is true. Equality is allowed in \(\le\).
Step 2
Why this answer is correct
The correct answer is A. कथन सही होगा / The statement will be true. Putting (x=6) gives \(36+4\le 40\), that is \(40\le 40\), which is true. Equality is allowed in \(\le\).
Step 3
Exam Tip
(x=6) रखने पर \(36+4\le 40\) यानी \(40\le 40\) सही है। \(\le\) में बराबरी स्वीकार होती है।
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असमानता (x-9>-4) का हल क्या है?
What is the solution of the inequality (x-9>-4)?
#linear inequalities
#negative constant
#addition
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A (x>5)
B (x<5)
C \(x\ge 5\)
D \(x\le 5\)
Explanation opens after your attempt
Step 1
Concept
Adding (9) to both sides gives (x>5). Addition does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Adding (9) to both sides gives (x>5). Addition does not change the sign.
Step 3
Exam Tip
दोनों पक्षों में (9) जोड़ने पर (x>5) मिलता है। जोड़ करने पर चिह्न नहीं बदलता।
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असमानता \(x+14\le -2\) का हल क्या है?
What is the solution of the inequality \(x+14\le -2\)?
#linear inequalities
#negative answer
#subtraction
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A \(x\le -16\)
B \(x\ge -16\)
C (x<-16)
D (x>-16)
Explanation opens after your attempt
Correct Answer
A. \(x\le -16\)
Step 1
Concept
Subtracting (14) from both sides gives \(x\le -16\). Even with a negative answer, subtraction does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le -16\). Subtracting (14) from both sides gives \(x\le -16\). Even with a negative answer, subtraction does not change the sign.
Step 3
Exam Tip
दोनों पक्षों से (14) घटाने पर \(x\le -16\) मिलता है। ऋणात्मक उत्तर आने पर भी घटाव से चिह्न नहीं बदलता।
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असमानता (11-2x<5) का हल क्या है?
What is the solution of the inequality (11-2x<5)?
#linear inequalities
#negative variable
#common mistake
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A (x>3)
B (x<3)
C \(x\ge 3\)
D \(x\le 3\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (11) gives (-2x<-6), so (x>3). Dividing by (-2) reverses the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Subtracting (11) gives (-2x<-6), so (x>3). Dividing by (-2) reverses the sign.
Step 3
Exam Tip
(11) घटाने पर (-2x<-6), इसलिए (x>3)। (-2) से भाग देने पर चिह्न पलटता है।
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असमानता \(6-5x\ge -9\) का हल क्या है?
What is the solution of the inequality \(6-5x\ge -9\)?
#linear inequalities
#negative variable
#negative constants
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A \(x\le 3\)
B \(x\ge 3\)
C (x<3)
D (x>3)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
Subtracting (6) gives \(-5x\ge -15\), then dividing by (-5) gives \(x\le 3\). Reverse the sign in negative division.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). Subtracting (6) gives \(-5x\ge -15\), then dividing by (-5) gives \(x\le 3\). Reverse the sign in negative division.
Step 3
Exam Tip
(6) घटाने पर \(-5x\ge -15\), फिर (-5) से भाग देने पर \(x\le 3\)। ऋणात्मक से भाग में चिह्न पलटें।
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असमानता (5x+6>3x+20) का हल क्या है?
What is the solution of the inequality (5x+6>3x+20)?
#linear inequalities
#variables both sides
#greater than
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A (x>7)
B (x<7)
C \(x\ge 7\)
D \(x\le 7\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (3x) gives (2x+6>20), so (x>7). Keep variable and constant terms separate.
Step 2
Why this answer is correct
The correct answer is A. (x>7). Subtracting (3x) gives (2x+6>20), so (x>7). Keep variable and constant terms separate.
Step 3
Exam Tip
(3x) घटाने पर (2x+6>20), इसलिए (x>7)। चर और स्थिर पद अलग रखें।
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असमानता \(2(x+7)\le 4x+6\) का हल क्या है?
What is the solution of the inequality \(2(x+7)\le 4x+6\)?
#linear inequalities
#brackets
#variable on right
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A \(x\ge 4\)
B \(x\le 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
From \(2x+14\le 4x+6\), we get \(8\le 2x\), so \(x\ge 4\). Even if the variable is on the right, write the answer with (x).
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). From \(2x+14\le 4x+6\), we get \(8\le 2x\), so \(x\ge 4\). Even if the variable is on the right, write the answer with (x).
Step 3
Exam Tip
\(2x+14\le 4x+6\) से \(8\le 2x\), इसलिए \(x\ge 4\)। दाईं ओर चर हो तो भी उत्तर (x) से लिखें।
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असमानता (9(x-1)>6x+12) का हल क्या है?
What is the solution of the inequality (9(x-1)>6x+12)?
#linear inequalities
#brackets
#strict inequality
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A (x>7)
B (x<7)
C \(x\ge 7\)
D \(x\le 7\)
Explanation opens after your attempt
Step 1
Concept
From (9x-9>6x+12), we get (3x>21), so (x>7). Pay attention to the minus sign in brackets.
Step 2
Why this answer is correct
The correct answer is A. (x>7). From (9x-9>6x+12), we get (3x>21), so (x>7). Pay attention to the minus sign in brackets.
Step 3
Exam Tip
(9x-9>6x+12) से (3x>21), इसलिए (x>7)। कोष्ठक में ऋण चिह्न पर ध्यान दें।
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किसी संख्या (x) में (18) जोड़ने पर परिणाम (50) से अधिक है। (x) का हल क्या है?
When (18) is added to a number (x), the result is greater than (50). What is the solution for (x)?
#linear inequalities
#word problem
#translation
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A (x>32)
B (x<32)
C \(x\ge 32\)
D \(x\le 32\)
Explanation opens after your attempt
Step 1
Concept
The situation gives (x+18>50), so (x>32). Convert words into the correct inequality.
Step 2
Why this answer is correct
The correct answer is A. (x>32). The situation gives (x+18>50), so (x>32). Convert words into the correct inequality.
Step 3
Exam Tip
स्थिति से (x+18>50), इसलिए (x>32)। शब्दों को सही असमानता में बदलें।
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राधा के पास (x) अंक हैं। यदि \(x+12\ge 45\), तो (x) का न्यूनतम मान क्या है?
Radha has (x) marks. If \(x+12\ge 45\), what is the minimum value of (x)?
#linear inequalities
#word problem
#minimum value
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A (33)
B (32)
C (45)
D (57)
Explanation opens after your attempt
Step 1
Concept
Subtracting (12) gives \(x\ge 33\), so the minimum value is (33). The sign \(\ge\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (33). Subtracting (12) gives \(x\ge 33\), so the minimum value is (33). The sign \(\ge\) includes the boundary value.
Step 3
Exam Tip
(12) घटाने पर \(x\ge 33\), इसलिए न्यूनतम मान (33) है। \(\ge\) में सीमा मान शामिल होता है।
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किसी संख्या (x) का तिगुना (27) से कम है। सही हल क्या है?
Three times a number (x) is less than (27). What is the correct solution?
#linear inequalities
#word problem
#multiplication
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A (x<9)
B (x>9)
C \(x\le 9\)
D \(x\ge 9\)
Explanation opens after your attempt
Step 1
Concept
Three times means (3x), so (3x<27) and (x<9). Less than means (<).
Step 2
Why this answer is correct
The correct answer is A. (x<9). Three times means (3x), so (3x<27) and (x<9). Less than means (<).
Step 3
Exam Tip
तिगुना (3x) होता है, इसलिए (3x<27) और (x<9)। कम है का अर्थ (<) है।
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किसी संख्या (x) से (7) घटाने पर परिणाम कम से कम (20) है। सही असमानता और हल क्या है?
When (7) is subtracted from a number (x), the result is at least (20). What are the correct inequality and solution?
#linear inequalities
#word problem
#at least
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A \(x-7\ge 20,\ x\ge 27\)
B (x-7>20,\ x>27)
C \(x+7\ge 20,\ x\ge 13\)
D \(x-7\le 20,\ x\le 27\)
Explanation opens after your attempt
Correct Answer
A. \(x-7\ge 20,\ x\ge 27\)
Step 1
Concept
At least means \(\ge\), so \(x-7\ge 20\) and \(x\ge 27\). Read word clues carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x-7\ge 20,\ x\ge 27\). At least means \(\ge\), so \(x-7\ge 20\) and \(x\ge 27\). Read word clues carefully.
Step 3
Exam Tip
कम से कम का अर्थ \(\ge\) है, इसलिए \(x-7\ge 20\) और \(x\ge 27\)। शब्द संकेतों को ध्यान से पढ़ें।
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असमानता \(2x+3\le 15\) का हल निकालने में सही क्रम कौन सा है?
Which is the correct order to solve \(2x+3\le 15\)?
#linear inequalities
#solving steps
#order
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A (3) घटाएं फिर (2) से भाग दें / Subtract (3) then divide by (2)
B (3) जोड़ें फिर (2) से भाग दें / Add (3) then divide by (2)
C (2) से भाग दें फिर (3) जोड़ें / Divide by (2) then add (3)
D (2) से गुणा करें फिर (3) घटाएं / Multiply by (2) then subtract (3)
Explanation opens after your attempt
Correct Answer
A. (3) घटाएं फिर (2) से भाग दें / Subtract (3) then divide by (2)
Step 1
Concept
First subtracting (3) gives \(2x\le 12\), then dividing by (2) gives \(x\le 6\). Use operations in reverse order.
Step 2
Why this answer is correct
The correct answer is A. (3) घटाएं फिर (2) से भाग दें / Subtract (3) then divide by (2). First subtracting (3) gives \(2x\le 12\), then dividing by (2) gives \(x\le 6\). Use operations in reverse order.
Step 3
Exam Tip
पहले (3) घटाने पर \(2x\le 12\), फिर (2) से भाग देने पर \(x\le 6\)। उल्टे क्रम में ऑपरेशन करें।
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असमानता (-x+9>1) का हल क्या है?
What is the solution of the inequality (-x+9>1)?
#linear inequalities
#negative variable
#sign reversal
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A (x<8)
B (x>8)
C \(x\le 8\)
D \(x\ge 8\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (9) gives (-x>-8), so dividing by (-1) gives (x<8). Reverse the sign when changing (-x) to (x).
Step 2
Why this answer is correct
The correct answer is A. (x<8). Subtracting (9) gives (-x>-8), so dividing by (-1) gives (x<8). Reverse the sign when changing (-x) to (x).
Step 3
Exam Tip
(9) घटाने पर (-x>-8), इसलिए (-1) से भाग देने पर (x<8)। (-x) को (x) बनाते समय चिह्न पलटें।
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असमानता (13<3x+1) का हल क्या है?
What is the solution of the inequality (13<3x+1)?
#linear inequalities
#rewrite inequality
#greater than
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A (x>4)
B (x<4)
C \(x\ge 4\)
D \(x\le 4\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (1) gives (12<3x), so (4<x), meaning (x>4). Read the sign correctly when rewriting the direction.
Step 2
Why this answer is correct
The correct answer is A. (x>4). Subtracting (1) gives (12<3x), so (4<x), meaning (x>4). Read the sign correctly when rewriting the direction.
Step 3
Exam Tip
(1) घटाने पर (12<3x), इसलिए (4<x) अर्थात (x>4)। दिशा बदलकर लिखते समय चिह्न सही पढ़ें।
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असमानता \(16\ge 2x+4\) का हल क्या है?
What is the solution of the inequality \(16\ge 2x+4\)?
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#rewrite inequality
#less equal
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A \(x\le 6\)
B \(x\ge 6\)
C (x<6)
D (x>6)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
Subtracting (4) gives \(12\ge 2x\), so \(6\ge x\), that is \(x\le 6\). Write the answer in standard form.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). Subtracting (4) gives \(12\ge 2x\), so \(6\ge x\), that is \(x\le 6\). Write the answer in standard form.
Step 3
Exam Tip
(4) घटाने पर \(12\ge 2x\), इसलिए \(6\ge x\) यानी \(x\le 6\)। उत्तर को सामान्य रूप में लिखें।
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असमानता (7x-12<2x+18) का हल क्या है?
What is the solution of the inequality (7x-12<2x+18)?
#linear inequalities
#variables both sides
#final practice
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A (x<6)
B (x>6)
C \(x\le 6\)
D \(x\ge 6\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (2x) gives (5x-12<18), so (x<6). Keeping variable terms on one side reduces mistakes.
Step 2
Why this answer is correct
The correct answer is A. (x<6). Subtracting (2x) gives (5x-12<18), so (x<6). Keeping variable terms on one side reduces mistakes.
Step 3
Exam Tip
(2x) घटाने पर (5x-12<18), इसलिए (x<6)। चर पदों को एक तरफ रखने से गलती कम होती है।
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असमानता \(5-3x\le -10\) का हल क्या है?
What is the solution of the inequality \(5-3x\le -10\)?
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#negative coefficient
#sign reversal
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A \(x\ge 5\)
B \(x\le 5\)
C (x>5)
D (x<5)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 5\)
Step 1
Concept
Subtracting (5) gives \(-3x\le -15\), so division by (-3) gives \(x\ge 5\). Dividing by a negative number reverses the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 5\). Subtracting (5) gives \(-3x\le -15\), so division by (-3) gives \(x\ge 5\). Dividing by a negative number reverses the sign.
Step 3
Exam Tip
(5) घटाने पर \(-3x\le -15\), इसलिए (-3) से भाग देने पर \(x\ge 5\)। ऋणात्मक संख्या से भाग देने पर चिह्न पलटता है।
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असमानता \(\frac{x-3}{5}>4\) का हल क्या है?
What is the solution of the inequality \(\frac{x-3}{5}>4\)?
#linear inequalities
#fraction
#positive denominator
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A (x>23)
B (x<23)
C \(x\ge 23\)
D \(x\le 23\)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (5) gives (x-3>20), so (x>23). Multiplying by a positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>23). Multiplying by (5) gives (x-3>20), so (x>23). Multiplying by a positive denominator does not change the sign.
Step 3
Exam Tip
(5) से गुणा करने पर (x-3>20), इसलिए (x>23)। धनात्मक हर से गुणा करने पर चिह्न नहीं बदलता।
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यदि (x) एक पूर्णांक है और \(4x-1\le 15\), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and \(4x-1\le 15\), what is the greatest possible (x)?
#linear inequalities
#integer solution
#greatest integer
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A (4)
B (3)
C (5)
D (15)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(4x\le 16\), so \(x\le 4\) and the greatest integer is (4). The sign \(\le\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives \(4x\le 16\), so \(x\le 4\) and the greatest integer is (4). The sign \(\le\) includes the boundary value.
Step 3
Exam Tip
असमानता से \(4x\le 16\), इसलिए \(x\le 4\) और सबसे बड़ा पूर्णांक (4) है। \(\le\) में सीमा मान शामिल होता है।
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