असमानता \(7-x\ge 2\) का सही हल कौन सा है?
Which is the correct solution of \(7-x\ge 2\)?
#linear inequalities
#negative coefficient
#solve
A \(x\le 5\)
B \(x\ge 5\)
C (x<9)
D (x>9)
Explanation opens after your attempt
Correct Answer
A. \(x\le 5\)
Step 1
Concept
From \(7-x\ge 2\), we get \(-x\ge -5\), and dividing by a negative gives \(x\le 5\). Reverse the sign when removing (-x).
Step 2
Why this answer is correct
The correct answer is A. \(x\le 5\). From \(7-x\ge 2\), we get \(-x\ge -5\), and dividing by a negative gives \(x\le 5\). Reverse the sign when removing (-x).
Step 3
Exam Tip
\(7-x\ge 2\) से \(-x\ge -5\) मिलता है और ऋणात्मक से भाग देने पर \(x\le 5\)। (-x) हटाते समय चिह्न पलटें।
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असमानता (3(x-2)<15) का सही हल कौन सा है?
Which is the correct solution of (3(x-2)<15)?
#linear inequalities
#bracket
#solve
A (x<7)
B (x>7)
C (x<5)
D (x>5)
Explanation opens after your attempt
Step 1
Concept
First divide by (3) to get (x-2<5), then (x<7). Keep the order correct in bracket questions.
Step 2
Why this answer is correct
The correct answer is A. (x<7). First divide by (3) to get (x-2<5), then (x<7). Keep the order correct in bracket questions.
Step 3
Exam Tip
पहले (3) से भाग देने पर (x-2<5) मिलता है और फिर (x<7)। कोष्ठक वाले प्रश्न में क्रम सही रखें।
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असमानता \(6x-5\ge 19\) का हल क्या है?
What is the solution of the inequality \(6x-5\ge 19\)?
#linear inequalities
#two step
#solve
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
First add (5) to both sides to get \(6x\ge 24\), then divide by (6). Division by a positive number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). First add (5) to both sides to get \(6x\ge 24\), then divide by (6). Division by a positive number does not change the sign.
Step 3
Exam Tip
पहले दोनों ओर (5) जोड़ें तो \(6x\ge 24\) मिलता है फिर (6) से भाग दें। धनात्मक भाग में चिह्न नहीं बदलता।
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असमानता (18<6x) का हल कौन सा है?
Which is the solution of (18<6x)?
#linear inequalities
#solve
#rewrite
A (x>3)
B (x<3)
C (x>24)
D (x<24)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (6) gives (3<x), that is (x>3). When rewriting, check the meaning of the direction.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Dividing both sides by (6) gives (3<x), that is (x>3). When rewriting, check the meaning of the direction.
Step 3
Exam Tip
दोनों ओर (6) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय दिशा का अर्थ जाँचें।
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असमानता \(\frac{x}{6}\le 2\) का हल क्या है?
What is the solution of \(\frac{x}{6}\le 2\)?
#linear inequalities
#fraction
#solve
A \(x\le 12\)
B \(x\ge 12\)
C \(x\le \frac{1}{3}\)
D \(x\ge \frac{1}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 12\)
Step 1
Concept
Multiplying both sides by (6) gives \(x\le 12\). Positive multiplication does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 12\). Multiplying both sides by (6) gives \(x\le 12\). Positive multiplication does not reverse the sign.
Step 3
Exam Tip
दोनों ओर (6) से गुणा करने पर \(x\le 12\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता।
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असमानता (x+11>11) का हल क्या है?
What is the solution of (x+11>11)?
#linear inequalities
#solve
#simple transformation
A (x>0)
B (x<0)
C (x>22)
D (x<22)
Explanation opens after your attempt
Step 1
Concept
Subtracting (11) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 2
Why this answer is correct
The correct answer is A. (x>0). Subtracting (11) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 3
Exam Tip
दोनों ओर (11) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए।
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असमानता \(2x+5\le 17\) का हल कौन सा है?
Which is the solution of \(2x+5\le 17\)?
#linear inequalities
#two step
#solve
A \(x\le 6\)
B \(x\ge 6\)
C \(x\le 11\)
D \(x\ge 11\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
First subtract (5), then divide by (2), giving \(x\le 6\). Keep the order correct in two-step questions.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). First subtract (5), then divide by (2), giving \(x\le 6\). Keep the order correct in two-step questions.
Step 3
Exam Tip
पहले (5) घटाएँ फिर (2) से भाग दें तो \(x\le 6\)। दो चरणों वाले प्रश्न में क्रम सही रखें।
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असमानता (9-x<4) का सही हल क्या है?
What is the correct solution of (9-x<4)?
#linear inequalities
#negative coefficient
#solve
A (x>5)
B (x<5)
C (x>13)
D (x<13)
Explanation opens after your attempt
Step 1
Concept
From (9-x<4), we get (-x<-5), and dividing by a negative gives (x>5). The sign reverses when removing (-x).
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (9-x<4), we get (-x<-5), and dividing by a negative gives (x>5). The sign reverses when removing (-x).
Step 3
Exam Tip
(9-x<4) से (-x<-5) और ऋणात्मक से भाग देने पर (x>5)। (-x) हटाते समय चिह्न पलटता है।
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असमानता \(x+4\ge 13\) का हल कौन सा है?
Which is the solution of \(x+4\ge 13\)?
#linear inequalities
#solve
#greater equal
A \(x\ge 9\)
B \(x\le 9\)
C (x>17)
D (x<17)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 9\)
Step 1
Concept
Subtracting (4) from both sides gives \(x\ge 9\). Addition or subtraction does not change the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 9\). Subtracting (4) from both sides gives \(x\ge 9\). Addition or subtraction does not change the direction.
Step 3
Exam Tip
दोनों ओर (4) घटाने पर \(x\ge 9\) मिलता है। जोड़ या घटाव से दिशा नहीं बदलती।
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असमानता \(4x\ge 20\) का हल क्या है?
What is the solution of \(4x\ge 20\)?
#linear inequalities
#division positive
#solve
A \(x\ge 5\)
B \(x\le 5\)
C \(x\ge 16\)
D \(x\le 16\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 5\)
Step 1
Concept
Dividing both sides by (4) gives \(x\ge 5\). Division by a positive number does not change the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 5\). Dividing both sides by (4) gives \(x\ge 5\). Division by a positive number does not change the direction.
Step 3
Exam Tip
दोनों ओर (4) से भाग देने पर \(x\ge 5\) मिलता है। धनात्मक भाग में दिशा नहीं बदलती।
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असमानता (x-8>2) का सही हल कौन सा है?
Which is the correct solution of (x-8>2)?
#linear inequalities
#solve
#greater than
A (x>10)
B (x<10)
C (x>6)
D (x<6)
Explanation opens after your attempt
Step 1
Concept
Adding (8) to both sides gives (x>10). Add the same number to remove the subtracted term.
Step 2
Why this answer is correct
The correct answer is A. (x>10). Adding (8) to both sides gives (x>10). Add the same number to remove the subtracted term.
Step 3
Exam Tip
दोनों ओर (8) जोड़ने पर (x>10) मिलता है। घटे हुए पद को हटाने के लिए वही संख्या जोड़ें।
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असमानता \(x+9\le 15\) का हल क्या है?
What is the solution of \(x+9\le 15\)?
#linear inequalities
#solve
#one step
A \(x\le 6\)
B \(x\ge 6\)
C \(x\le 24\)
D \(x\ge 24\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
Subtracting (9) from both sides gives \(x\le 6\). Addition or subtraction does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). Subtracting (9) from both sides gives \(x\le 6\). Addition or subtraction does not change the sign.
Step 3
Exam Tip
दोनों ओर (9) घटाने पर \(x\le 6\) मिलता है। जोड़ या घटाव से चिह्न नहीं बदलता।
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असमानता \(4-x\le 0\) का सही हल कौन सा है?
Which is the correct solution of \(4-x\le 0\)?
#linear inequalities
#negative coefficient
#solve
A \(x\le 4\)
B \(x\ge 4\)
C (x<4)
D (x>4)
Explanation opens after your attempt
Correct Answer
B. \(x\ge 4\)
Step 1
Concept
From \(4-x\le 0\), we get \(-x\le -4\), and dividing by a negative gives \(x\ge 4\). Reverse the sign when removing (-x).
Step 2
Why this answer is correct
The correct answer is B. \(x\ge 4\). From \(4-x\le 0\), we get \(-x\le -4\), and dividing by a negative gives \(x\ge 4\). Reverse the sign when removing (-x).
Step 3
Exam Tip
\(4-x\le 0\) से \(-x\le -4\) मिलता है और ऋणात्मक से भाग देने पर \(x\ge 4\)। (-x) हटाते समय चिह्न पलटें।
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असमानता (2(x+3)\ge 14) का सही हल कौन सा है?
Which is the correct solution of (2(x+3)\ge 14)?
#linear inequalities
#bracket
#solve
A \(x\ge 4\)
B \(x\le 4\)
C \(x\ge 10\)
D \(x\le 10\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
First divide by (2) to get \(x+3\ge 7\), then \(x\ge 4\). Keep the order correct in bracket questions.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). First divide by (2) to get \(x+3\ge 7\), then \(x\ge 4\). Keep the order correct in bracket questions.
Step 3
Exam Tip
पहले (2) से भाग देने पर \(x+3\ge 7\) और फिर \(x\ge 4\) मिलता है। कोष्ठक वाले प्रश्न में क्रम सही रखें।
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असमानता (5x-7<18) का हल क्या है?
What is the solution of the inequality (5x-7<18)?
#linear inequalities
#two step
#solve
A (x<5)
B (x>5)
C (x<11)
D (x>11)
Explanation opens after your attempt
Step 1
Concept
First add (7) to both sides to get (5x<25), then divide by (5). Division by a positive number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<5). First add (7) to both sides to get (5x<25), then divide by (5). Division by a positive number does not change the sign.
Step 3
Exam Tip
पहले दोनों ओर (7) जोड़ें तो (5x<25) मिलता है फिर (5) से भाग दें। धनात्मक भाग में चिह्न नहीं बदलता।
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असमानता (12<4x) का हल कौन सा है?
Which is the solution of (12<4x)?
#linear inequalities
#solve
#rewrite
A (x>3)
B (x<3)
C (x>16)
D (x<16)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (4) gives (3<x), that is (x>3). When rewriting, check the meaning of the direction.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Dividing both sides by (4) gives (3<x), that is (x>3). When rewriting, check the meaning of the direction.
Step 3
Exam Tip
दोनों ओर (4) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय दिशा का अर्थ जाँचें।
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असमानता \(\frac{x}{4}\le 3\) का हल क्या है?
What is the solution of \(\frac{x}{4}\le 3\)?
#linear inequalities
#fraction
#solve
A \(x\le 12\)
B \(x\ge 12\)
C \(x\le \frac{3}{4}\)
D \(x\ge \frac{3}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 12\)
Step 1
Concept
Multiplying both sides by (4) gives \(x\le 12\). Positive multiplication does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 12\). Multiplying both sides by (4) gives \(x\le 12\). Positive multiplication does not reverse the sign.
Step 3
Exam Tip
दोनों ओर (4) से गुणा करने पर \(x\le 12\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता।
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असमानता (x+9>9) का हल क्या है?
What is the solution of (x+9>9)?
#linear inequalities
#solve
#simple transformation
A (x>0)
B (x<0)
C (x>18)
D (x<18)
Explanation opens after your attempt
Step 1
Concept
Subtracting (9) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 2
Why this answer is correct
The correct answer is A. (x>0). Subtracting (9) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 3
Exam Tip
दोनों ओर (9) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए।
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असमानता \(6x+4\le 22\) का हल कौन सा है?
Which is the solution of \(6x+4\le 22\)?
#linear inequalities
#two step
#solve
A \(x\le 3\)
B \(x\ge 3\)
C \(x\le 4\)
D \(x\ge 4\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
First subtract (4), then divide by (6), giving \(x\le 3\). Keep the order correct in two-step questions.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). First subtract (4), then divide by (6), giving \(x\le 3\). Keep the order correct in two-step questions.
Step 3
Exam Tip
पहले (4) घटाएँ फिर (6) से भाग दें तो \(x\le 3\)। दो चरणों वाले प्रश्न में क्रम सही रखें।
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असमानता (8-x<3) का सही हल क्या है?
What is the correct solution of (8-x<3)?
#linear inequalities
#negative coefficient
#solve
A (x>5)
B (x<5)
C (x>11)
D (x<11)
Explanation opens after your attempt
Step 1
Concept
From (8-x<3), we get (-x<-5), and dividing by a negative gives (x>5). The sign reverses when removing (-x).
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (8-x<3), we get (-x<-5), and dividing by a negative gives (x>5). The sign reverses when removing (-x).
Step 3
Exam Tip
(8-x<3) से (-x<-5) मिलता है और ऋणात्मक से भाग देने पर (x>5)। (-x) हटाते समय चिह्न पलटता है।
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असमानता \(x+2\ge 9\) का हल कौन सा है?
Which is the solution of \(x+2\ge 9\)?
#linear inequalities
#solve
#greater equal
A \(x\ge 7\)
B \(x\le 7\)
C (x>11)
D (x<11)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 7\)
Step 1
Concept
Subtracting (2) from both sides gives \(x\ge 7\). Addition or subtraction does not change the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 7\). Subtracting (2) from both sides gives \(x\ge 7\). Addition or subtraction does not change the direction.
Step 3
Exam Tip
दोनों ओर (2) घटाने पर \(x\ge 7\) मिलता है। जोड़ या घटाव से दिशा नहीं बदलती।
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असमानता \(-5x\ge 15\) का सही हल क्या है?
What is the correct solution of \(-5x\ge 15\)?
#linear inequalities
#negative division
#solve
A \(x\ge -3\)
B \(x\le -3\)
C \(x\ge 3\)
D \(x\le 3\)
Explanation opens after your attempt
Correct Answer
B. \(x\le -3\)
Step 1
Concept
Dividing by (-5) reverses the sign, so \(x\le -3\). Be careful with negative coefficients.
Step 2
Why this answer is correct
The correct answer is B. \(x\le -3\). Dividing by (-5) reverses the sign, so \(x\le -3\). Be careful with negative coefficients.
Step 3
Exam Tip
(-5) से भाग देने पर चिह्न पलटता है इसलिए \(x\le -3\)। ऋणात्मक गुणांक पर सावधानी रखें।
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असमानता (3x<21) का हल क्या है?
What is the solution of (3x<21)?
#linear inequalities
#division positive
#solve
A (x<7)
B (x>7)
C (x<18)
D (x>18)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (3) gives (x<7). Division by a positive number keeps the sign the same.
Step 2
Why this answer is correct
The correct answer is A. (x<7). Dividing both sides by (3) gives (x<7). Division by a positive number keeps the sign the same.
Step 3
Exam Tip
दोनों ओर (3) से भाग देने पर (x<7) मिलता है। धनात्मक भाग में चिह्न वैसा ही रहता है।
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असमानता \(x-5\ge 1\) का सही हल कौन सा है?
Which is the correct solution of \(x-5\ge 1\)?
#linear inequalities
#solve
#greater equal
A \(x\ge 6\)
B \(x\le 6\)
C \(x\ge 4\)
D \(x\le 4\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 6\)
Step 1
Concept
Adding (5) to both sides gives \(x\ge 6\). Addition does not change the direction of the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 6\). Adding (5) to both sides gives \(x\ge 6\). Addition does not change the direction of the sign.
Step 3
Exam Tip
दोनों ओर (5) जोड़ने पर \(x\ge 6\) मिलता है। जोड़ में चिह्न की दिशा नहीं बदलती।
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असमानता (x+6<14) का हल क्या है?
What is the solution of (x+6<14)?
#linear inequalities
#solve
#one step
A (x<8)
B (x>8)
C (x<20)
D (x>20)
Explanation opens after your attempt
Step 1
Concept
Subtracting (6) from both sides gives (x<8). First remove the extra term.
Step 2
Why this answer is correct
The correct answer is A. (x<8). Subtracting (6) from both sides gives (x<8). First remove the extra term.
Step 3
Exam Tip
दोनों ओर (6) घटाने पर (x<8) मिलता है। पहले अतिरिक्त पद हटाएँ।
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असमानता (9<3x+3) का सही हल क्या है?
What is the correct solution of the inequality (9<3x+3)?
#linear inequalities
#solve
#rewrite inequality
A (x>2)
B (x<2)
C (x>4)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
First subtract (3) from both sides to get (6<3x), then divide by (3) to get (x>2). When rewriting an inequality, always check the meaning of its direction.
Step 2
Why this answer is correct
The correct answer is A. (x>2). First subtract (3) from both sides to get (6<3x), then divide by (3) to get (x>2). When rewriting an inequality, always check the meaning of its direction.
Step 3
Exam Tip
पहले दोनों ओर (3) घटाएँ तो (6<3x) मिलता है और फिर (3) से भाग देने पर (x>2) आता है। असमानता को पलटकर लिखते समय दिशा का अर्थ जरूर जाँचें।
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असमानता \(7-3x\ge 1\) का हल कौन सा है?
Which is the solution of \(7-3x\ge 1\)?
#linear inequalities
#negative coefficient
#solve
A \(x\le 2\)
B \(x\ge 2\)
C (x<2)
D (x>2)
Explanation opens after your attempt
Correct Answer
A. \(x\le 2\)
Step 1
Concept
From \(7-3x\ge 1\), we get \(-3x\ge -6\), and dividing by (-3) gives \(x\le 2\). The sign reverses when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 2\). From \(7-3x\ge 1\), we get \(-3x\ge -6\), and dividing by (-3) gives \(x\le 2\). The sign reverses when dividing by a negative number.
Step 3
Exam Tip
\(7-3x\ge 1\) से \(-3x\ge -6\) और (-3) से भाग देने पर \(x\le 2\) मिलता है। ऋणात्मक संख्या से भाग देते समय चिह्न पलटता है।
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असमानता (6<2x) का हल कौन सा है?
Which is the solution of (6<2x)?
#linear inequalities
#solve
#rewrite
A (x>3)
B (x<3)
C (x>12)
D (x<12)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.
Step 3
Exam Tip
दोनों ओर (2) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय चिह्न की दिशा अर्थ से जाँचें।
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असमानता \(\frac{x}{3}\le 2\) का हल क्या है?
What is the solution of \(\frac{x}{3}\le 2\)?
#linear inequalities
#fraction
#solve
A \(x\le 6\)
B \(x\ge 6\)
C \(x\le \frac{2}{3}\)
D \(x\ge \frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.
Step 3
Exam Tip
दोनों ओर (3) से गुणा करने पर \(x\le 6\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता।
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असमानता (x+7>7) का हल क्या है?
What is the solution of (x+7>7)?
#linear inequalities
#solve
#simple transformation
A (x>0)
B (x<0)
C (x>14)
D (x<14)
Explanation opens after your attempt
Step 1
Concept
Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 2
Why this answer is correct
The correct answer is A. (x>0). Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 3
Exam Tip
दोनों ओर (7) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए।
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