असमानता (x+3>7) का हल क्या है?
What is the solution of the inequality (x+3>7)?
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A (x>4)
B (x<4)
C (x>10)
D (x<10)
Explanation opens after your attempt
Step 1
Concept
Subtracting (3) from both sides of (x+3>7) gives (x>4). In exams remember that subtracting the same number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>4). Subtracting (3) from both sides of (x+3>7) gives (x>4). In exams remember that subtracting the same number does not change the sign.
Step 3
Exam Tip
(x+3>7) में दोनों पक्षों से (3) घटाने पर (x>4) मिलता है। परीक्षा में समान संख्या घटाने से चिन्ह नहीं बदलता।
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असमानता \(x-5\le 2\) का हल चुनिए।
Choose the solution of the inequality \(x-5\le 2\).
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A \(x\le 7\)
B \(x\ge 7\)
C \(x\le -3\)
D \(x\ge -3\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 7\)
Step 1
Concept
Adding (5) to both sides of \(x-5\le 2\) gives \(x\le 7\). Addition keeps the inequality sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 7\). Adding (5) to both sides of \(x-5\le 2\) gives \(x\le 7\). Addition keeps the inequality sign unchanged.
Step 3
Exam Tip
\(x-5\le 2\) में दोनों पक्षों में (5) जोड़ने पर \(x\le 7\) मिलता है। जोड़ने पर असमानता का चिन्ह वही रहता है।
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असमानता \(3x\ge 18\) का हल ज्ञात कीजिए।
Find the solution of the inequality \(3x\ge 18\).
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A \(x\ge 6\)
B \(x\le 6\)
C \(x\ge 21\)
D \(x\le 21\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 6\)
Step 1
Concept
Dividing \(3x\ge 18\) by (3) gives \(x\ge 6\). The sign stays the same when dividing by a positive coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 6\). Dividing \(3x\ge 18\) by (3) gives \(x\ge 6\). The sign stays the same when dividing by a positive coefficient.
Step 3
Exam Tip
\(3x\ge 18\) में (3) से भाग देने पर \(x\ge 6\) मिलता है। धनात्मक गुणांक हटाते समय चिन्ह वैसा ही रहता है।
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असमानता \(-2x\le 8\) का सही हल क्या है?
What is the correct solution of \(-2x\le 8\)?
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A \(x\ge -4\)
B \(x\le -4\)
C \(x\ge 4\)
D \(x\le 4\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge -4\)
Step 1
Concept
Dividing \(-2x\le 8\) by (-2) reverses the sign and gives \(x\ge -4\). This sign reversal is a very common exam mistake.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge -4\). Dividing \(-2x\le 8\) by (-2) reverses the sign and gives \(x\ge -4\). This sign reversal is a very common exam mistake.
Step 3
Exam Tip
\(-2x\le 8\) में (-2) से भाग देने पर चिन्ह उलटकर \(x\ge -4\) मिलता है। यह आसान प्रश्नों में सबसे सामान्य गलती होती है।
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असमानता (5x+1>16) को हल कीजिए।
Solve the inequality (5x+1>16).
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A (x>3)
B (x<3)
C (x>17)
D (x<17)
Explanation opens after your attempt
Step 1
Concept
First subtract (1) to get (5x>15), then divide by (5) to get (x>3). Removing the constant term first makes solving easier.
Step 2
Why this answer is correct
The correct answer is A. (x>3). First subtract (1) to get (5x>15), then divide by (5) to get (x>3). Removing the constant term first makes solving easier.
Step 3
Exam Tip
पहले (1) घटाने पर (5x>15) और फिर (5) से भाग देने पर (x>3) मिलता है। पहले स्थिर पद हटाना आसान रहता है।
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असमानता \(4x-7\le 9\) का हल क्या है?
What is the solution of \(4x-7\le 9\)?
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A \(x\le 4\)
B \(x\ge 4\)
C \(x\le 16\)
D \(x\ge 16\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 4\)
Step 1
Concept
Adding (7) gives \(4x\le 16\), and dividing by (4) gives \(x\le 4\). Dividing by positive (4) keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 4\). Adding (7) gives \(4x\le 16\), and dividing by (4) gives \(x\le 4\). Dividing by positive (4) keeps the sign unchanged.
Step 3
Exam Tip
(7) जोड़ने पर \(4x\le 16\) और (4) से भाग देने पर \(x\le 4\) मिलता है। धनात्मक (4) से भाग देने पर चिन्ह नहीं बदलता।
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असमानता (6-2x>0) का हल चुनिए।
Choose the solution of (6-2x>0).
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A (x<3)
B (x>3)
C (x<-3)
D (x> -3)
Explanation opens after your attempt
Step 1
Concept
From (6-2x>0), we get (-2x>-6), and dividing by (-2) gives (x<3). Reverse the sign when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. (x<3). From (6-2x>0), we get (-2x>-6), and dividing by (-2) gives (x<3). Reverse the sign when dividing by a negative number.
Step 3
Exam Tip
(6-2x>0) से (-2x>-6) मिलता है और (-2) से भाग देने पर (x<3) मिलता है। ऋणात्मक से भाग देते समय चिन्ह पलटता है।
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असमानता \(7-3x\ge 1\) का हल क्या है?
What is the solution of \(7-3x\ge 1\)?
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A \(x\le 2\)
B \(x\ge 2\)
C \(x\le -2\)
D \(x\ge -2\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 2\)
Step 1
Concept
\(7-3x\ge 1\) gives \(-3x\ge -6\), then \(x\le 2\). The inequality sign must reverse with a negative coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 2\). \(7-3x\ge 1\) gives \(-3x\ge -6\), then \(x\le 2\). The inequality sign must reverse with a negative coefficient.
Step 3
Exam Tip
\(7-3x\ge 1\) से \(-3x\ge -6\) और फिर \(x\le 2\) मिलता है। ऋणात्मक गुणांक पर चिन्ह उलटना जरूरी है।
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असमानता \(2x+5\le x+9\) का हल ज्ञात कीजिए।
Find the solution of \(2x+5\le x+9\).
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A \(x\le 4\)
B \(x\ge 4\)
C \(x\le 14\)
D \(x\ge 14\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 4\)
Step 1
Concept
Subtracting (x) and (5) from both sides gives \(x\le 4\). Keep variable terms on one side and constants on the other.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 4\). Subtracting (x) and (5) from both sides gives \(x\le 4\). Keep variable terms on one side and constants on the other.
Step 3
Exam Tip
दोनों पक्षों से (x) और (5) घटाने पर \(x\le 4\) मिलता है। चर पदों को एक ओर और संख्याओं को दूसरी ओर रखें।
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असमानता (3x-2>x+6) का सही हल क्या है?
What is the correct solution of (3x-2>x+6)?
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A (x>4)
B (x<4)
C (x>2)
D (x<2)
Explanation opens after your attempt
Step 1
Concept
From (3x-2>x+6), we get (2x>8), so (x>4). Subtracting like terms does not change the inequality sign.
Step 2
Why this answer is correct
The correct answer is A. (x>4). From (3x-2>x+6), we get (2x>8), so (x>4). Subtracting like terms does not change the inequality sign.
Step 3
Exam Tip
(3x-2>x+6) से (2x>8) मिलता है इसलिए (x>4) है। समान पद घटाने से चिन्ह नहीं बदलता।
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असमानता \(4x+3\ge 2x+11\) का हल चुनिए।
Choose the solution of \(4x+3\ge 2x+11\).
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A \(x\ge 4\)
B \(x\le 4\)
C \(x\ge 7\)
D \(x\le 7\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
\(4x+3\ge 2x+11\) gives \(2x\ge 8\), hence \(x\ge 4\). Simplify fully before choosing the answer.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). \(4x+3\ge 2x+11\) gives \(2x\ge 8\), hence \(x\ge 4\). Simplify fully before choosing the answer.
Step 3
Exam Tip
\(4x+3\ge 2x+11\) से \(2x\ge 8\) और इसलिए \(x\ge 4\) मिलता है। सरल बनाने के बाद ही उत्तर चुनें।
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असमानता (5x-4<3x+2) का हल क्या है?
What is the solution of (5x-4<3x+2)?
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A (x<3)
B (x>3)
C (x< -3)
D (x> -3)
Explanation opens after your attempt
Step 1
Concept
From (5x-4<3x+2), we get (2x<6), so (x<3). Combining variable terms correctly is essential.
Step 2
Why this answer is correct
The correct answer is A. (x<3). From (5x-4<3x+2), we get (2x<6), so (x<3). Combining variable terms correctly is essential.
Step 3
Exam Tip
(5x-4<3x+2) से (2x<6) मिलता है इसलिए (x<3) है। चर पदों को ठीक से मिलाना जरूरी है।
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असमानता \(9-x\le 5\) का हल बताइए।
State the solution of \(9-x\le 5\).
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A \(x\ge 4\)
B \(x\le 4\)
C \(x\ge 14\)
D \(x\le 14\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
\(9-x\le 5\) gives \(-x\le -4\), and dividing by (-1) gives \(x\ge 4\). Reverse the sign when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). \(9-x\le 5\) gives \(-x\le -4\), and dividing by (-1) gives \(x\ge 4\). Reverse the sign when dividing by a negative number.
Step 3
Exam Tip
\(9-x\le 5\) से \(-x\le -4\) मिलता है और (-1) से भाग देने पर \(x\ge 4\) है। ऋणात्मक से भाग देने पर चिन्ह उलटें।
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असमानता \(\frac{x}{2}>3\) का हल क्या है?
What is the solution of \(\frac{x}{2}>3\)?
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A (x>6)
B (x<6)
C \(x> \frac{3}{2}\)
D \(x< \frac{3}{2}\)
Explanation opens after your attempt
Step 1
Concept
Multiplying both sides of \(\frac{x}{2}>3\) by (2) gives (x>6). Multiplication by positive (2) keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x>6). Multiplying both sides of \(\frac{x}{2}>3\) by (2) gives (x>6). Multiplication by positive (2) keeps the sign unchanged.
Step 3
Exam Tip
\(\frac{x}{2}>3\) में दोनों पक्षों को (2) से गुणा करने पर (x>6) मिलता है। धनात्मक (2) से गुणा करने पर चिन्ह नहीं बदलता।
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असमानता \(\frac{x}{3}\le 4\) का हल चुनिए।
Choose the solution of \(\frac{x}{3}\le 4\).
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A \(x\le 12\)
B \(x\ge 12\)
C \(x\le \frac{4}{3}\)
D \(x\ge \frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 12\)
Step 1
Concept
Multiplying both sides by (3) gives \(x\le 12\). When the denominator is positive, the sign does not change.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 12\). Multiplying both sides by (3) gives \(x\le 12\). When the denominator is positive, the sign does not change.
Step 3
Exam Tip
दोनों पक्षों को (3) से गुणा करने पर \(x\le 12\) मिलता है। हर हटाते समय वह धनात्मक हो तो चिन्ह नहीं बदलता।
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असमानता \(\frac{x+1}{2}\ge 5\) का हल ज्ञात कीजिए।
Find the solution of \(\frac{x+1}{2}\ge 5\).
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A \(x\ge 9\)
B \(x\le 9\)
C \(x\ge 11\)
D \(x\le 11\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 9\)
Step 1
Concept
Multiplying by (2) gives \(x+1\ge 10\), and subtracting (1) gives \(x\ge 9\). Solving step by step reduces mistakes.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 9\). Multiplying by (2) gives \(x+1\ge 10\), and subtracting (1) gives \(x\ge 9\). Solving step by step reduces mistakes.
Step 3
Exam Tip
(2) से गुणा करने पर \(x+1\ge 10\) और (1) घटाने पर \(x\ge 9\) मिलता है। क्रम से हल करने पर गलती कम होती है।
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असमानता \(\frac{x-2}{5}<1\) का सही हल क्या है?
What is the correct solution of \(\frac{x-2}{5}<1\)?
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A (x<7)
B (x>7)
C (x<3)
D (x>3)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (5) gives (x-2<5), and adding (2) gives (x<7). A positive denominator keeps the inequality sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x<7). Multiplying by (5) gives (x-2<5), and adding (2) gives (x<7). A positive denominator keeps the inequality sign unchanged.
Step 3
Exam Tip
(5) से गुणा करने पर (x-2<5) और (2) जोड़ने पर (x<7) मिलता है। धनात्मक हर हटाते समय चिन्ह वैसा ही रहता है।
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असमानता \(\frac{2x}{3}>4\) का हल बताइए।
State the solution of \(\frac{2x}{3}>4\).
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A (x>6)
B (x<6)
C \(x> \frac{8}{3}\)
D \(x< \frac{8}{3}\)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (3) gives (2x>12), and dividing by (2) gives (x>6). Remove fractions to form a simple linear inequality.
Step 2
Why this answer is correct
The correct answer is A. (x>6). Multiplying by (3) gives (2x>12), and dividing by (2) gives (x>6). Remove fractions to form a simple linear inequality.
Step 3
Exam Tip
(3) से गुणा करने पर (2x>12) और (2) से भाग देने पर (x>6) मिलता है। भिन्न हटाकर सरल रैखिक रूप बनाएं।
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असमानता (2(x+3)>14) का हल कौन सा है?
Which is the solution of (2(x+3)>14)?
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A (x>4)
B (x<4)
C (x>10)
D (x<10)
Explanation opens after your attempt
Step 1
Concept
Writing (2(x+3)>14) as (2x+6>14) gives (2x>8), so (x>4). Open brackets first.
Step 2
Why this answer is correct
The correct answer is A. (x>4). Writing (2(x+3)>14) as (2x+6>14) gives (2x>8), so (x>4). Open brackets first.
Step 3
Exam Tip
(2(x+3)>14) को (2x+6>14) लिखने पर (2x>8) और (x>4) मिलता है। कोष्ठक पहले खोलें।
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असमानता (5(x-1)<3x+7) का सही हल क्या है?
What is the correct solution of (5(x-1)<3x+7)?
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#brackets
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A (x<6)
B (x>6)
C (x<1)
D (x>1)
Explanation opens after your attempt
Step 1
Concept
(5x-5<3x+7) gives (2x<12), hence (x<6). Watch the signs while opening brackets.
Step 2
Why this answer is correct
The correct answer is A. (x<6). (5x-5<3x+7) gives (2x<12), hence (x<6). Watch the signs while opening brackets.
Step 3
Exam Tip
(5x-5<3x+7) से (2x<12) और (x<6) मिलता है। कोष्ठक खोलते समय चिन्हों पर ध्यान दें।
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असमानता (2(3x-1)>4x+6) का हल क्या है?
What is the solution of (2(3x-1)>4x+6)?
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A (x>4)
B (x<4)
C (x>2)
D (x<2)
Explanation opens after your attempt
Step 1
Concept
(2(3x-1)>4x+6) gives (6x-2>4x+6), then (2x>8). Therefore (x>4) is correct.
Step 2
Why this answer is correct
The correct answer is A. (x>4). (2(3x-1)>4x+6) gives (6x-2>4x+6), then (2x>8). Therefore (x>4) is correct.
Step 3
Exam Tip
(2(3x-1)>4x+6) से (6x-2>4x+6) और फिर (2x>8) मिलता है। अतः (x>4) सही है।
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हल (x<5) को अंतराल रूप में कैसे लिखेंगे?
How do we write the solution (x<5) in interval form?
#linear-inequalities
#interval-notation
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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
In (x<5), (5) is not included, so the interval is (\(-\infty,5\)). Use a round bracket for (<).
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,5\)). In (x<5), (5) is not included, so the interval is (\(-\infty,5\)). Use a round bracket for (<).
Step 3
Exam Tip
(x<5) में (5) शामिल नहीं है इसलिए खुला अंतराल (\(-\infty,5\)) होगा। (<) के लिए कोष्ठक गोल रखें।
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हल \(x\ge -2\) का अंतराल रूप क्या है?
What is the interval form of the solution \(x\ge -2\)?
#linear-inequalities
#interval-notation
#class-11
#easy
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A \([-2,\infty\))
B (\(-2,\infty\))
C (\(-\infty,-2]\)
D (\(-\infty,-2\))
Explanation opens after your attempt
Correct Answer
A. \([-2,\infty\))
Step 1
Concept
In \(x\ge -2\), (-2) is included, so \([-2,\infty\)) is correct. Infinity always takes a round bracket.
Step 2
Why this answer is correct
The correct answer is A. \([-2,\infty\)). In \(x\ge -2\), (-2) is included, so \([-2,\infty\)) is correct. Infinity always takes a round bracket.
Step 3
Exam Tip
\(x\ge -2\) में (-2) शामिल है इसलिए \([-2,\infty\)) सही है। \(\infty\) के साथ हमेशा गोल कोष्ठक आता है।
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असमानता \(2x-1\ge 7\) के हल का अंतराल रूप क्या है?
What is the interval form of the solution of \(2x-1\ge 7\)?
#linear-inequalities
#interval-notation
#class-11
#easy
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A \([4,\infty\))
B (\(4,\infty\))
C (\(-\infty,4]\)
D (\(-\infty,4\))
Explanation opens after your attempt
Correct Answer
A. \([4,\infty\))
Step 1
Concept
\(2x-1\ge 7\) gives \(2x\ge 8\), so \(x\ge 4\). The symbol \(\ge\) includes (4).
Step 2
Why this answer is correct
The correct answer is A. \([4,\infty\)). \(2x-1\ge 7\) gives \(2x\ge 8\), so \(x\ge 4\). The symbol \(\ge\) includes (4).
Step 3
Exam Tip
\(2x-1\ge 7\) से \(2x\ge 8\) और \(x\ge 4\) मिलता है। \(\ge\) के कारण (4) शामिल होगा।
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असमानता (x-1>2) के प्राकृतिक संख्या हलों में सबसे छोटी संख्या कौन सी है?
What is the smallest natural number solution of (x-1>2)?
#linear-inequalities
#natural-number-solutions
#class-11
#easy
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A (4)
B (3)
C (2)
D (1)
Explanation opens after your attempt
Step 1
Concept
(x-1>2) gives (x>3), so the smallest natural number is (4). A strict inequality does not include the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (4). (x-1>2) gives (x>3), so the smallest natural number is (4). A strict inequality does not include the boundary value.
Step 3
Exam Tip
(x-1>2) से (x>3) मिलता है इसलिए सबसे छोटी प्राकृतिक संख्या (4) है। सख्त असमानता में सीमा मान शामिल नहीं होता।
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असमानता \(x+2\le 6\) के धनात्मक पूर्णांक हलों की संख्या कितनी है?
How many positive integer solutions does \(x+2\le 6\) have?
#linear-inequalities
#integer-solutions
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#easy
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A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(x+2\le 6\) gives \(x\le 4\), and the positive integers are (1,2,3,4). Do not count (0) as a positive integer.
Step 2
Why this answer is correct
The correct answer is A. (4). \(x+2\le 6\) gives \(x\le 4\), and the positive integers are (1,2,3,4). Do not count (0) as a positive integer.
Step 3
Exam Tip
\(x+2\le 6\) से \(x\le 4\) मिलता है और धनात्मक पूर्णांक (1,2,3,4) हैं। गिनते समय (0) को धनात्मक पूर्णांक न मानें।
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असमानता \(3x\ge 7\) को संतुष्ट करने वाला सबसे छोटा पूर्णांक कौन सा है?
Which is the least integer satisfying \(3x\ge 7\)?
#linear-inequalities
#integer-solutions
#class-11
#easy
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A (3)
B (2)
C (1)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(3x\ge 7\) gives \(x\ge \frac{7}{3}\), so the least integer is (3). Take the first integer above the boundary.
Step 2
Why this answer is correct
The correct answer is A. (3). \(3x\ge 7\) gives \(x\ge \frac{7}{3}\), so the least integer is (3). Take the first integer above the boundary.
Step 3
Exam Tip
\(3x\ge 7\) से \(x\ge \frac{7}{3}\) मिलता है इसलिए सबसे छोटा पूर्णांक (3) है। सीमा से ऊपर पहला पूर्णांक लें।
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असमानता (5-x>1) को संतुष्ट करने वाला सबसे बड़ा पूर्णांक कौन सा है?
Which is the greatest integer satisfying (5-x>1)?
#linear-inequalities
#integer-solutions
#class-11
#easy
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A (3)
B (4)
C (5)
D (1)
Explanation opens after your attempt
Step 1
Concept
(5-x>1) gives (-x>-4), then (x<4). Therefore the greatest integer is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). (5-x>1) gives (-x>-4), then (x<4). Therefore the greatest integer is (3).
Step 3
Exam Tip
(5-x>1) से (-x>-4) और (x<4) मिलता है। अतः सबसे बड़ा पूर्णांक (3) है।
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यदि (x=3) हो तो कौन सी असमानता सत्य है?
If (x=3), which inequality is true?
#linear-inequalities
#verification
#class-11
#easy
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A (x+2<6)
B (2x>7)
C (x-5>0)
D \(3x\le 8\)
Explanation opens after your attempt
Correct Answer
A. (x+2<6)
Step 1
Concept
Putting (x=3), we get (x+2=5), and (5<6) is true. Substitute the given value directly while checking options.
Step 2
Why this answer is correct
The correct answer is A. (x+2<6). Putting (x=3), we get (x+2=5), and (5<6) is true. Substitute the given value directly while checking options.
Step 3
Exam Tip
(x=3) रखने पर (x+2=5) और (5<6) सत्य है। विकल्प जांचते समय दिए गए मान को सीधे रखें।
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यदि (x=5) हो तो कौन सी असमानता असत्य है?
If (x=5), which inequality is false?
#linear-inequalities
#verification
#class-11
#easy
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A (x-1>5)
B \(x+1\ge 6\)
C \(2x\le 10\)
D (x<8)
Explanation opens after your attempt
Correct Answer
A. (x-1>5)
Step 1
Concept
Putting (x=5), (x-1=4), and (4>5) is false. Check true and false options carefully.
Step 2
Why this answer is correct
The correct answer is A. (x-1>5). Putting (x=5), (x-1=4), and (4>5) is false. Check true and false options carefully.
Step 3
Exam Tip
(x=5) रखने पर (x-1=4) और (4>5) असत्य है। सत्य और असत्य विकल्पों को अलग-अलग जांचें।
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असमानता \(x+7\ge 7\) का हल क्या है?
What is the solution of \(x+7\ge 7\)?
#linear-inequalities
#boundary-value
#class-11
#easy
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A \(x\ge 0\)
B \(x\le 0\)
C \(x\ge 14\)
D \(x\le 14\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 0\)
Step 1
Concept
Subtracting (7) from both sides gives \(x\ge 0\). Include the boundary value when equality is present.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 0\). Subtracting (7) from both sides gives \(x\ge 0\). Include the boundary value when equality is present.
Step 3
Exam Tip
दोनों पक्षों से (7) घटाने पर \(x\ge 0\) मिलता है। बराबरी वाला चिन्ह हो तो सीमा मान शामिल करें।
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असमानता (x-4< -1) का हल चुनिए।
Choose the solution of (x-4< -1).
#linear-inequalities
#negative-constants
#class-11
#easy
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A (x<3)
B (x>3)
C (x< -5)
D (x> -5)
Explanation opens after your attempt
Step 1
Concept
Adding (4) to both sides gives (x<3). Even with negative numbers, addition does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<3). Adding (4) to both sides gives (x<3). Even with negative numbers, addition does not change the sign.
Step 3
Exam Tip
दोनों पक्षों में (4) जोड़ने पर (x<3) मिलता है। ऋणात्मक संख्या के साथ भी जोड़ने से चिन्ह नहीं बदलता।
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असमानता (x+6> -2) का सही हल क्या है?
What is the correct solution of (x+6> -2)?
#linear-inequalities
#negative-constants
#class-11
#easy
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A (x> -8)
B (x< -8)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. (x> -8)
Step 1
Concept
Subtracting (6) from both sides gives (x>-8). Handle integer signs carefully.
Step 2
Why this answer is correct
The correct answer is A. (x> -8). Subtracting (6) from both sides gives (x>-8). Handle integer signs carefully.
Step 3
Exam Tip
दोनों पक्षों से (6) घटाने पर (x>-8) मिलता है। पूर्णांकों के चिन्ह सावधानी से संभालें।
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असमानता (-3x>12) को हल करते समय कौन सा नियम लागू होगा?
Which rule applies while solving (-3x>12)?
#linear-inequalities
#sign-change-rule
#class-11
#easy
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A (-3) से भाग देने पर चिन्ह उलटेगा / Dividing by (-3) reverses the sign
B (-3) से भाग देने पर चिन्ह वही रहेगा / Dividing by (-3) keeps the sign same
C (12) जोड़ने पर चिन्ह उलटेगा / Adding (12) reverses the sign
D (3) से गुणा करने पर चिन्ह उलटेगा / Multiplying by (3) reverses the sign
Explanation opens after your attempt
Correct Answer
A. (-3) से भाग देने पर चिन्ह उलटेगा / Dividing by (-3) reverses the sign
Step 1
Concept
In (-3x>12), we divide by the negative number (-3), so the sign reverses. This rule is very important in inequalities.
Step 2
Why this answer is correct
The correct answer is A. (-3) से भाग देने पर चिन्ह उलटेगा / Dividing by (-3) reverses the sign. In (-3x>12), we divide by the negative number (-3), so the sign reverses. This rule is very important in inequalities.
Step 3
Exam Tip
(-3x>12) में ऋणात्मक संख्या (-3) से भाग देना होगा इसलिए चिन्ह उलटेगा। यह नियम असमानताओं में बहुत महत्वपूर्ण है।
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असमानता \(8+2x\le 20\) का हल क्या है?
What is the solution of \(8+2x\le 20\)?
#linear-inequalities
#two-step
#class-11
#easy
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A \(x\le 6\)
B \(x\ge 6\)
C \(x\le 14\)
D \(x\ge 14\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
\(8+2x\le 20\) gives \(2x\le 12\), so \(x\le 6\). Move the constant term to the other side and simplify.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). \(8+2x\le 20\) gives \(2x\le 12\), so \(x\le 6\). Move the constant term to the other side and simplify.
Step 3
Exam Tip
\(8+2x\le 20\) से \(2x\le 12\) और \(x\le 6\) मिलता है। स्थिर पद को दूसरी ओर ले जाकर सरल करें।
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एक संख्या में (5) जोड़ने पर परिणाम (12) से अधिक है। संख्या के लिए सही असमानता कौन सी है?
When (5) is added to a number, the result is greater than (12). Which inequality is correct for the number?
#linear-inequalities
#word-problem
#class-11
#easy
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A (x+5>12)
B (x-5>12)
C (5x>12)
D (x+12>5)
Explanation opens after your attempt
Correct Answer
A. (x+5>12)
Step 1
Concept
Let the number be (x). Adding (5) gives (x+5), and greater than means (>). Convert words into algebra first.
Step 2
Why this answer is correct
The correct answer is A. (x+5>12). Let the number be (x). Adding (5) gives (x+5), and greater than means (>). Convert words into algebra first.
Step 3
Exam Tip
संख्या को (x) मानने पर (5) जोड़ना (x+5) है और अधिक का अर्थ (>) है। शब्दों को पहले बीजीय रूप में बदलें।
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किसी संख्या का (2) गुना (18) से कम है। संख्या के लिए हल क्या है?
Twice a number is less than (18). What is the solution for the number?
#linear-inequalities
#word-problem
#class-11
#easy
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A (x<9)
B (x>9)
C (x<18)
D (x>18)
Explanation opens after your attempt
Step 1
Concept
The statement gives (2x<18), and dividing by (2) gives (x<9). Dividing by a positive number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<9). The statement gives (2x<18), and dividing by (2) gives (x<9). Dividing by a positive number does not change the sign.
Step 3
Exam Tip
वाक्य से (2x<18) बनता है और (2) से भाग देने पर (x<9) मिलता है। धनात्मक संख्या से भाग देने पर चिन्ह नहीं बदलता।
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रवि के पास (x) रुपये हैं और (30) रुपये खर्च करने के बाद उसके पास कम से कम (70) रुपये बचते हैं। (x) के लिए असमानता क्या है?
Ravi has (x) rupees and after spending (30) rupees, at least (70) rupees remain. What is the inequality for (x)?
#linear-inequalities
#word-problem
#class-11
#easy
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A \(x-30\ge 70\)
B \(x+30\ge 70\)
C \(x-70\ge 30\)
D \(30-x\ge 70\)
Explanation opens after your attempt
Correct Answer
A. \(x-30\ge 70\)
Step 1
Concept
After spending, the amount is (x-30), and at least (70) means \(\ge 70\). In words, at least is written using \(\ge\).
Step 2
Why this answer is correct
The correct answer is A. \(x-30\ge 70\). After spending, the amount is (x-30), and at least (70) means \(\ge 70\). In words, at least is written using \(\ge\).
Step 3
Exam Tip
खर्च करने के बाद राशि (x-30) होगी और कम से कम (70) का अर्थ \(\ge 70\) है। भाषा में कम से कम को \(\ge\) से लिखें।
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एक पेन की कीमत (x) रुपये है और (4) पेन की कुल कीमत (100) रुपये से अधिक नहीं है। (x) का हल क्या है?
The price of one pen is (x) rupees and the cost of (4) pens is not more than (100) rupees. What is the solution for (x)?
#linear-inequalities
#word-problem
#class-11
#easy
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A \(x\le 25\)
B \(x\ge 25\)
C (x<25)
D (x>25)
Explanation opens after your attempt
Correct Answer
A. \(x\le 25\)
Step 1
Concept
The situation gives \(4x\le 100\), so \(x\le 25\). Not more than means \(\le\).
Step 2
Why this answer is correct
The correct answer is A. \(x\le 25\). The situation gives \(4x\le 100\), so \(x\le 25\). Not more than means \(\le\).
Step 3
Exam Tip
स्थिति से \(4x\le 100\) बनता है इसलिए \(x\le 25\) है। अधिक नहीं का अर्थ \(\le\) होता है।
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किसी संख्या से (8) घटाने पर परिणाम (0) से बड़ा या बराबर है। संख्या के लिए हल क्या है?
When (8) is subtracted from a number, the result is greater than or equal to (0). What is the solution for the number?
#linear-inequalities
#word-problem
#class-11
#easy
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A \(x\ge 8\)
B \(x\le 8\)
C (x>8)
D (x<8)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 8\)
Step 1
Concept
The statement gives \(x-8\ge 0\), and adding (8) gives \(x\ge 8\). Use \(\ge\) for greater than or equal to.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 8\). The statement gives \(x-8\ge 0\), and adding (8) gives \(x\ge 8\). Use \(\ge\) for greater than or equal to.
Step 3
Exam Tip
वाक्य से \(x-8\ge 0\) बनता है और (8) जोड़ने पर \(x\ge 8\) मिलता है। बराबर या बड़ा के लिए \(\ge\) प्रयोग करें।
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असमानता \(3x+4\le 13\) में (x=3) रखने पर क्या निष्कर्ष है?
What is the conclusion after putting (x=3) in \(3x+4\le 13\)?
#linear-inequalities
#verification
#class-11
#easy
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A (x=3) हल है / (x=3) is a solution
B (x=3) हल नहीं है / (x=3) is not a solution
C (x=3) से (13<13) मिलता है / (x=3) gives (13<13)
D (x=3) से (13>13) मिलता है / (x=3) gives (13>13)
Explanation opens after your attempt
Correct Answer
A. (x=3) हल है / (x=3) is a solution
Step 1
Concept
Putting (x=3), (3x+4=13), and \(13\le 13\) is true. Equality is included in \(\le\).
Step 2
Why this answer is correct
The correct answer is A. (x=3) हल है / (x=3) is a solution. Putting (x=3), (3x+4=13), and \(13\le 13\) is true. Equality is included in \(\le\).
Step 3
Exam Tip
(x=3) रखने पर (3x+4=13) और \(13\le 13\) सत्य है। \(\le\) में बराबरी भी शामिल होती है।
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असमानता \(x\le -3\) के लिए कौन सा मान हल है?
Which value is a solution of \(x\le -3\)?
#linear-inequalities
#verification
#class-11
#easy
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A (-4)
B (0)
C (-2)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(-4\le -3\) is true, so (-4) is a solution. Compare negative numbers using the number line.
Step 2
Why this answer is correct
The correct answer is A. (-4). \(-4\le -3\) is true, so (-4) is a solution. Compare negative numbers using the number line.
Step 3
Exam Tip
\(-4\le -3\) सत्य है इसलिए (-4) हल है। ऋणात्मक संख्याओं की तुलना संख्या रेखा से करें।
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असमानता \(7x+2\le 23\) का हल क्या है?
What is the solution of the inequality \(7x+2\le 23\)?
#linear-inequalities
#algebraic-solution
#class-11
#easy
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A \(x\le 3\)
B \(x\ge 3\)
C \(x\le 21\)
D \(x\ge 21\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
Subtracting (2) from \(7x+2\le 23\) gives \(7x\le 21\), and dividing by (7) gives \(x\le 3\). Division by a positive number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). Subtracting (2) from \(7x+2\le 23\) gives \(7x\le 21\), and dividing by (7) gives \(x\le 3\). Division by a positive number does not change the sign.
Step 3
Exam Tip
\(7x+2\le 23\) में (2) घटाने पर \(7x\le 21\) और (7) से भाग देने पर \(x\le 3\) मिलता है। धनात्मक संख्या से भाग देने पर चिन्ह नहीं बदलता।
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असमानता (-4x+5<17) का सही हल चुनिए।
Choose the correct solution of (-4x+5<17).
#linear-inequalities
#sign-change
#class-11
#easy
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A (x>-3)
B (x<-3)
C (x>3)
D (x<3)
Explanation opens after your attempt
Step 1
Concept
Subtracting (5) gives (-4x<12), and dividing by (-4) gives (x>-3). The inequality sign reverses when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. (x>-3). Subtracting (5) gives (-4x<12), and dividing by (-4) gives (x>-3). The inequality sign reverses when dividing by a negative number.
Step 3
Exam Tip
(5) घटाने पर (-4x<12) मिलता है और (-4) से भाग देने पर (x>-3) मिलता है। ऋणात्मक संख्या से भाग देने पर असमानता का चिन्ह उलटता है।
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असमानता \(\frac{x+3}{4}<2\) का हल क्या है?
What is the solution of \(\frac{x+3}{4}<2\)?
#linear-inequalities
#fractions
#class-11
#easy
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A (x<5)
B (x>5)
C (x<8)
D (x>8)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (4) gives (x+3<8), and subtracting (3) gives (x<5). The sign stays the same when clearing a positive denominator.
Step 2
Why this answer is correct
The correct answer is A. (x<5). Multiplying by (4) gives (x+3<8), and subtracting (3) gives (x<5). The sign stays the same when clearing a positive denominator.
Step 3
Exam Tip
(4) से गुणा करने पर (x+3<8) और (3) घटाने पर (x<5) मिलता है। धनात्मक हर हटाते समय चिन्ह वही रहता है।
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असमानता \(2x+1\le 5x-8\) का हल ज्ञात कीजिए।
Find the solution of \(2x+1\le 5x-8\).
#linear-inequalities
#variables-both-sides
#class-11
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A \(x\ge 3\)
B \(x\le 3\)
C \(x\ge -3\)
D \(x\le -3\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
Subtracting (2x) from both sides gives \(1\le 3x-8\), then \(9\le 3x\). Hence \(x\ge 3\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). Subtracting (2x) from both sides gives \(1\le 3x-8\), then \(9\le 3x\). Hence \(x\ge 3\) is correct.
Step 3
Exam Tip
दोनों पक्षों से (2x) जोड़ने के बजाय (2x) घटाने पर \(1\le 3x-8\) और फिर \(9\le 3x\) मिलता है। इसलिए \(x\ge 3\) सही है।
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किसी संख्या में (3) जोड़ने पर परिणाम (16) से अधिक नहीं है। संख्या का हल क्या है?
When (3) is added to a number, the result is not more than (16). What is the solution for the number?
#linear-inequalities
#word-problem
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A \(x\le 13\)
B \(x\ge 13\)
C (x<13)
D (x>13)
Explanation opens after your attempt
Correct Answer
A. \(x\le 13\)
Step 1
Concept
The statement gives \(x+3\le 16\), and subtracting (3) gives \(x\le 13\). Not more than means \(\le\).
Step 2
Why this answer is correct
The correct answer is A. \(x\le 13\). The statement gives \(x+3\le 16\), and subtracting (3) gives \(x\le 13\). Not more than means \(\le\).
Step 3
Exam Tip
वाक्य से \(x+3\le 16\) बनता है और (3) घटाने पर \(x\le 13\) मिलता है। अधिक नहीं का अर्थ \(\le\) होता है।
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असमानता \(9-2x\le 1\) का हल क्या है?
What is the solution of the inequality \(9-2x\le 1\)?
#linear-inequalities
#sign-change
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#easy
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A \(x\ge 4\)
B \(x\le 4\)
C \(x\ge -4\)
D \(x\le -4\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
Subtracting (9) from \(9-2x\le 1\) gives \(-2x\le -8\), and dividing by (-2) gives \(x\ge 4\). The sign reverses when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). Subtracting (9) from \(9-2x\le 1\) gives \(-2x\le -8\), and dividing by (-2) gives \(x\ge 4\). The sign reverses when dividing by a negative number.
Step 3
Exam Tip
\(9-2x\le 1\) में (9) घटाने पर \(-2x\le -8\) मिलता है और (-2) से भाग देने पर \(x\ge 4\) मिलता है। ऋणात्मक संख्या से भाग देने पर चिन्ह उलटता है।
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