यदि संख्या रेखा पर हल \([ -1,\infty\)) है तो कौन सी असमानता सही है?
If the solution on the number line is \([ -1,\infty\)), which inequality is correct?
#interval to inequality
#closed ray
#number line
A (x>-1)
B \(x\ge -1\)
C (x<-1)
D \(x\le -1\)
Explanation opens after your attempt
Correct Answer
B. \(x\ge -1\)
Step 1
Concept
(-1) is included and the line goes right, so \(x\ge -1\). In exams, read ([ ) as including equality.
Step 2
Why this answer is correct
The correct answer is B. \(x\ge -1\). (-1) is included and the line goes right, so \(x\ge -1\). In exams, read ([ ) as including equality.
Step 3
Exam Tip
(-1) शामिल है और रेखा दाईं ओर जाती है इसलिए \(x\ge -1\) होगा। परीक्षा में ([ ) को बराबरी सहित पढ़ें।
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अंतराल (\(-\infty,3]\) को असमानता के रूप में कैसे लिखेंगे?
How do you write the interval (\(-\infty,3]\) as an inequality?
#interval to inequality
#number line
#linear inequalities
A (x<3)
B \(x\le 3\)
C (x>3)
D \(x\ge 3\)
Explanation opens after your attempt
Correct Answer
B. \(x\le 3\)
Step 1
Concept
The number (3) is included and all smaller numbers are taken. In exams, match (]) with \(\le\).
Step 2
Why this answer is correct
The correct answer is B. \(x\le 3\). The number (3) is included and all smaller numbers are taken. In exams, match (]) with \(\le\).
Step 3
Exam Tip
(3) शामिल है और उससे छोटी सभी संख्याएँ ली गई हैं। परीक्षा में (]) को \(\le\) से मिलाएँ।
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संख्या रेखा पर ([ -4,3 )) का सही असमता रूप कौन सा है?
Which inequality form correctly represents ([-4,3)) on the number line?
#linear-inequalities
#interval-to-inequality
#number-line
A (-4<x<3)
B \(-4\le x<3\)
C \(-4<x\le 3\)
D \(-4\le x\le 3\)
Explanation opens after your attempt
Correct Answer
B. \(-4\le x<3\)
Step 1
Concept
The square bracket includes (-4) and the parenthesis excludes (3). Therefore the form is \(-4\le x<3\).
Step 2
Why this answer is correct
The correct answer is B. \(-4\le x<3\). The square bracket includes (-4) and the parenthesis excludes (3). Therefore the form is \(-4\le x<3\).
Step 3
Exam Tip
वर्ग कोष्ठक (-4) को शामिल करता है और गोल कोष्ठक (3) को बाहर रखता है। इसलिए \(-4\le x<3\) होगा।
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कौन सा विकल्प \(x\in (-15,-7)\) को असमता रूप में सही लिखता है?
Which option correctly writes \(x\in (-15,-7)\) in inequality form?
#linear-inequalities
#interval-to-inequality
#open-interval
A \(-15\le x\le -7\)
B (-15<x<-7)
C \(-15\le x<-7\)
D \(-15<x\le -7\)
Explanation opens after your attempt
Correct Answer
B. (-15<x<-7)
Step 1
Concept
Both sides have parentheses so both endpoints are excluded. Thus (-15<x<-7) is correct.
Step 2
Why this answer is correct
The correct answer is B. (-15<x<-7). Both sides have parentheses so both endpoints are excluded. Thus (-15<x<-7) is correct.
Step 3
Exam Tip
दोनों ओर गोल कोष्ठक हैं इसलिए दोनों सीमाएँ शामिल नहीं हैं। अतः (-15<x<-7) सही है।
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यदि (x\in (6,15]) है तो असमता रूप कौन सा है?
If (x\in (6,15]), what is the inequality form?
#linear-inequalities
#interval-to-inequality
#mixed-endpoints
A \(6\le x\le 15\)
B (6<x<15)
C \(6<x\le 15\)
D \(6\le x<15\)
Explanation opens after your attempt
Correct Answer
C. \(6<x\le 15\)
Step 1
Concept
(6) is not included but (15) is included. Therefore \(6<x\le 15\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(6<x\le 15\). (6) is not included but (15) is included. Therefore \(6<x\le 15\) is correct.
Step 3
Exam Tip
(6) शामिल नहीं है लेकिन (15) शामिल है। इसलिए \(6<x\le 15\) सही है।
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अंतराल \((-\infty,9)\) संख्या रेखा पर किस असमता को दर्शाता है?
Which inequality is represented by the interval \((-\infty,9)\) on the number line?
#linear-inequalities
#interval-to-inequality
#number-line
A (x<9)
B \(x\le 9\)
C (x>9)
D \(x\ge 9\)
Explanation opens after your attempt
Correct Answer
B. \(x\le 9\)
Step 1
Concept
The square bracket shows that (9) is included and values extend toward \(-\infty\). Hence it is \(x\le 9\).
Step 2
Why this answer is correct
The correct answer is B. \(x\le 9\). The square bracket shows that (9) is included and values extend toward \(-\infty\). Hence it is \(x\le 9\).
Step 3
Exam Tip
वर्ग कोष्ठक बताता है कि (9) शामिल है और \(-\infty\) की ओर छोटी संख्याएँ हैं। इसलिए \(x\le 9\) होगा।
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अंतराल \((-\infty, -\frac{1}{2})\) संख्या रेखा पर किस असमता को दर्शाता है?
Which inequality is represented by the interval \((-\infty, -\frac{1}{2}]\) on the number line?
#linear-inequalities
#interval-to-inequality
#fraction-boundary
A \(x<-\frac{1}{2}\)
B \(x\le -\frac{1}{2}\)
C \(x>-\frac{1}{2}\)
D \(x\ge -\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(x\le -\frac{1}{2}\)
Step 1
Concept
The square bracket shows that \(-\frac{1}{2}\) is included, and the values extend toward \(-\infty\). Hence \(x\le -\frac{1}{2}\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(x\le -\frac{1}{2}\). The square bracket shows that \(-\frac{1}{2}\) is included, and the values extend toward \(-\infty\). Hence \(x\le -\frac{1}{2}\) is correct.
Step 3
Exam Tip
वर्ग कोष्ठक बताता है कि \(-\frac{1}{2}\) शामिल है और \(-\infty\) की ओर छोटी संख्याएँ हैं। इसलिए \(x\le -\frac{1}{2}\) सही है।
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कौन सा विकल्प \(x\in (-7,-2)\) को असमता रूप में सही लिखता है?
Which option correctly writes \(x\in (-7,-2)\) in inequality form?
#linear-inequalities
#interval-to-inequality
#open-interval
A \(-7\le x\le -2\)
B (-7<x<-2)
C \(-7\le x<-2\)
D \(-7<x\le -2\)
Explanation opens after your attempt
Correct Answer
B. (-7<x<-2)
Step 1
Concept
Both sides have parentheses, so both endpoints are excluded. Thus (-7<x<-2) is correct.
Step 2
Why this answer is correct
The correct answer is B. (-7<x<-2). Both sides have parentheses, so both endpoints are excluded. Thus (-7<x<-2) is correct.
Step 3
Exam Tip
दोनों ओर गोल कोष्ठक हैं इसलिए दोनों सीमाएँ शामिल नहीं हैं। अतः (-7<x<-2) सही है।
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अंतराल \([0,\infty\)) संख्या रेखा पर किस असमता को दर्शाता है?
Which inequality is represented by the interval \([0,\infty\)) on the number line?
#linear-inequalities
#nonnegative
#interval-to-inequality
A (x>0)
B (x<0)
C \(x\ge 0\)
D \(x\le 0\)
Explanation opens after your attempt
Correct Answer
C. \(x\ge 0\)
Step 1
Concept
The interval \([0,\infty\)) includes (0) and all numbers to the right. Therefore it is \(x\ge 0\).
Step 2
Why this answer is correct
The correct answer is C. \(x\ge 0\). The interval \([0,\infty\)) includes (0) and all numbers to the right. Therefore it is \(x\ge 0\).
Step 3
Exam Tip
\([0,\infty\)) में (0) शामिल है और दाईं ओर सभी संख्याएँ हैं। इसलिए यह \(x\ge 0\) है।
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यदि \(x\in [2,9]\) है तो असमता रूप कौन सा है?
If \(x\in [2,9]\), what is the inequality form?
#linear-inequalities
#interval-to-inequality
#compound
A (2<x<9)
B \(2\le x<9\)
C \(2<x\le 9\)
D \(2\le x\le 9\)
Explanation opens after your attempt
Correct Answer
B. \(2\le x<9\)
Step 1
Concept
The bracket ([2) shows (2) is included and (9)) shows (9) is not included. Hence \(2\le x<9\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(2\le x<9\). The bracket ([2) shows (2) is included and (9)) shows (9) is not included. Hence \(2\le x<9\) is correct.
Step 3
Exam Tip
([2) बताता है कि (2) शामिल है और (9)) बताता है कि (9) शामिल नहीं है। इसलिए \(2\le x<9\) सही है।
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(x\in (-2,4]) का असमता रूप कौन सा है?
What is the inequality form of (x\in (-2,4])?
#linear-inequalities
#interval-to-inequality
#compound
A \(-2<x\le 4\)
B \(-2\le x<4\)
C \(-2\le x\le 4\)
D (-2<x<4)
Explanation opens after your attempt
Correct Answer
A. \(-2<x\le 4\)
Step 1
Concept
A parenthesis gives a strict inequality and a square bracket gives an inclusive inequality. Therefore \(-2<x\le 4\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(-2<x\le 4\). A parenthesis gives a strict inequality and a square bracket gives an inclusive inequality. Therefore \(-2<x\le 4\) is correct.
Step 3
Exam Tip
गोल कोष्ठक पर कठोर असमता और वर्ग कोष्ठक पर बराबरी सहित असमता लगती है। इसलिए \(-2<x\le 4\) सही है।
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अंतराल ([-2,5)) को असमता के रूप में कैसे लिखेंगे?
How is interval ([-2,5)) written as an inequality?
#interval-to-inequality
#notation
#concept
A \(-2\leq x<5\)
B \(-2<x\leq 5\)
C (-2<x<5)
D \(-2\leq x\leq 5\)
Explanation opens after your attempt
Correct Answer
A. \(-2\leq x<5\)
Step 1
Concept
In ([-2,5)), (-2) is included and (5) is not included. A square bracket includes equality.
Step 2
Why this answer is correct
The correct answer is A. \(-2\leq x<5\). In ([-2,5)), (-2) is included and (5) is not included. A square bracket includes equality.
Step 3
Exam Tip
([-2,5)) में (-2) शामिल है और (5) शामिल नहीं है। वर्ग कोष्ठक के लिए बराबरी शामिल होती है।
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किस विकल्प का हल (\(- \infty,2]\) है?
Which option has solution (\(- \infty,2]\)?
#linear-inequalities
#interval-to-inequality
#closed-end
A (x<2)
B \(x\le 2\)
C (x>2)
D \(x\ge 2\)
Explanation opens after your attempt
Correct Answer
B. \(x\le 2\)
Step 1
Concept
The interval (\(- \infty,2]\) includes (2) and all smaller numbers. Hence \(x\le 2\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(x\le 2\). The interval (\(- \infty,2]\) includes (2) and all smaller numbers. Hence \(x\le 2\) is correct.
Step 3
Exam Tip
(\(- \infty,2]\) में (2) शामिल है और उससे छोटी सभी संख्याएँ आती हैं। इसलिए \(x\le 2\) सही है।
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