असमानता (x>8) का सही अर्थ क्या है?
What is the correct meaning of the inequality (x>8)?
#linear inequalities
#symbol meaning
#greater than
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A (x) संख्या (8) से बड़ी है / (x) is greater than (8)
B (x) संख्या (8) से छोटी है / (x) is less than (8)
C (x) संख्या (8) के बराबर है / (x) is equal to (8)
D (x) संख्या (8) से बड़ी या बराबर है / (x) is greater than or equal to (8)
Explanation opens after your attempt
Correct Answer
A. (x) संख्या (8) से बड़ी है / (x) is greater than (8)
Step 1
Concept
The sign (>) means the value on the left is greater. In exams the open side of the sign faces the greater number.
Step 2
Why this answer is correct
The correct answer is A. (x) संख्या (8) से बड़ी है / (x) is greater than (8). The sign (>) means the value on the left is greater. In exams the open side of the sign faces the greater number.
Step 3
Exam Tip
चिह्न (>) बताता है कि बाईं ओर का मान बड़ा है। परीक्षा में चिह्न की खुली तरफ बड़ी संख्या होती है।
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असमानता \(y\le -3\) में (y=-3) के लिए कथन कैसा है?
For (y=-3), how is the statement \(y\le -3\)?
#linear inequalities
#less equal
#boundary value
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A सत्य / True
B असत्य / False
C निर्धारित नहीं / Not determined
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
A. सत्य / True
Step 1
Concept
The sign \(\le\) includes equality, so \(-3\le -3\) is true. Always check the boundary value separately.
Step 2
Why this answer is correct
The correct answer is A. सत्य / True. The sign \(\le\) includes equality, so \(-3\le -3\) is true. Always check the boundary value separately.
Step 3
Exam Tip
\(\le\) में बराबरी शामिल होती है इसलिए \(-3\le -3\) सत्य है। सीमा मान को हमेशा अलग से जाँचें।
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इनमें से कौन सा कथन रैखिक असमानता है?
Which of the following statements is a linear inequality?
#linear inequalities
#identify linear
#basics
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A \(5x-2\ge 13\)
B \(x^2+1>0\)
C \(\frac{1}{x}<4\)
D \(xy\le 6\)
Explanation opens after your attempt
Correct Answer
A. \(5x-2\ge 13\)
Step 1
Concept
In \(5x-2\ge 13\), the variable has power (1), so it is a linear inequality. Forms with \(x^2\) or (xy) are not linear.
Step 2
Why this answer is correct
The correct answer is A. \(5x-2\ge 13\). In \(5x-2\ge 13\), the variable has power (1), so it is a linear inequality. Forms with \(x^2\) or (xy) are not linear.
Step 3
Exam Tip
\(5x-2\ge 13\) में चर की घात (1) है इसलिए यह रैखिक असमानता है। \(x^2\) या (xy) वाला रूप रैखिक नहीं माना जाता।
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कौन सा मान \(x\ge 5\) को संतुष्ट नहीं करता?
Which value does not satisfy \(x\ge 5\)?
#linear inequalities
#solution check
#greater equal
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A (5)
B (6)
C (10)
D (4)
Explanation opens after your attempt
Step 1
Concept
The number (4) is less than (5), so it does not satisfy \(x\ge 5\). Check options by substituting them directly.
Step 2
Why this answer is correct
The correct answer is D. (4). The number (4) is less than (5), so it does not satisfy \(x\ge 5\). Check options by substituting them directly.
Step 3
Exam Tip
(4) संख्या (5) से छोटी है इसलिए \(x\ge 5\) को संतुष्ट नहीं करती। विकल्पों को सीधे असमानता में रखकर जाँचें।
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वाक्य (t) (11) से कम है को असमानता में कैसे लिखेंगे?
How do we write the sentence (t) is less than (11) as an inequality?
#linear inequalities
#translation
#less than
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A (t>11)
B (t<11)
C \(t\ge 11\)
D (t=11)
Explanation opens after your attempt
Step 1
Concept
Less than means (<). In word-based questions connect the key phrase with the correct symbol.
Step 2
Why this answer is correct
The correct answer is B. (t<11). Less than means (<). In word-based questions connect the key phrase with the correct symbol.
Step 3
Exam Tip
से कम है का अर्थ (<) होता है। भाषा वाले प्रश्नों में मुख्य शब्द को प्रतीक से जोड़ें।
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वाक्य (z) (9) से कम नहीं है का सही रूप कौन सा है?
What is the correct form of the sentence (z) is not less than (9)?
#linear inequalities
#translation
#at least
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A (z<9)
B \(z\le 9\)
C \(z\ge 9\)
D \(z\ne 9\)
Explanation opens after your attempt
Correct Answer
C. \(z\ge 9\)
Step 1
Concept
Not less than means at least (9), so \(z\ge 9\). Such sentences include equality.
Step 2
Why this answer is correct
The correct answer is C. \(z\ge 9\). Not less than means at least (9), so \(z\ge 9\). Such sentences include equality.
Step 3
Exam Tip
कम नहीं है का अर्थ कम से कम (9) है इसलिए \(z\ge 9\)। ऐसे वाक्यों में बराबरी शामिल होती है।
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यदि (a>2) है तो दोनों ओर (5) जोड़ने पर कौन सी असमानता मिलेगी?
If (a>2), which inequality is obtained by adding (5) to both sides?
#linear inequalities
#addition property
#operation
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A (a+5>7)
B (a+5<7)
C (a-5>7)
D (5a>7)
Explanation opens after your attempt
Correct Answer
A. (a+5>7)
Step 1
Concept
Adding the same number does not change the direction of an inequality. Apply the same operation to both sides.
Step 2
Why this answer is correct
The correct answer is A. (a+5>7). Adding the same number does not change the direction of an inequality. Apply the same operation to both sides.
Step 3
Exam Tip
समान संख्या जोड़ने पर असमानता की दिशा नहीं बदलती। दोनों पक्षों पर एक ही क्रिया करें।
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यदि \(b\le 12\) है तो दोनों ओर (4) घटाने पर क्या होगा?
If \(b\le 12\), what happens after subtracting (4) from both sides?
#linear inequalities
#subtraction property
#less equal
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A \(b-4\le 8\)
B \(b-4\ge 8\)
C \(b+4\le 8\)
D \(4b\le 8\)
Explanation opens after your attempt
Correct Answer
A. \(b-4\le 8\)
Step 1
Concept
Subtracting the same number does not change the sign. In subtraction only the value changes, not the direction.
Step 2
Why this answer is correct
The correct answer is A. \(b-4\le 8\). Subtracting the same number does not change the sign. In subtraction only the value changes, not the direction.
Step 3
Exam Tip
समान संख्या घटाने से चिह्न नहीं बदलता। घटाव में केवल मान बदलता है दिशा नहीं।
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यदि (p<3) है तो दोनों ओर (6) से गुणा करने पर क्या मिलेगा?
If (p<3), what do we get after multiplying both sides by (6)?
#linear inequalities
#positive multiplication
#property
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A (6p<18)
B (6p>18)
C (p<18)
D (p>18)
Explanation opens after your attempt
Correct Answer
A. (6p<18)
Step 1
Concept
Multiplication by the positive number (6) keeps the direction the same. The sign reverses only in negative multiplication.
Step 2
Why this answer is correct
The correct answer is A. (6p<18). Multiplication by the positive number (6) keeps the direction the same. The sign reverses only in negative multiplication.
Step 3
Exam Tip
धनात्मक संख्या (6) से गुणा करने पर दिशा वही रहती है। केवल ऋणात्मक गुणा में चिह्न पलटता है।
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यदि (q<5) है तो दोनों ओर (-2) से गुणा करने पर सही परिणाम क्या है?
If (q<5), what is the correct result after multiplying both sides by (-2)?
#linear inequalities
#negative multiplication
#sign reversal
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A (-2q<-10)
B (-2q>-10)
C (2q>-10)
D (-q<10)
Explanation opens after your attempt
Correct Answer
B. (-2q>-10)
Step 1
Concept
Multiplying by a negative number reverses the inequality sign. While multiplying by (-2), changing the direction is necessary.
Step 2
Why this answer is correct
The correct answer is B. (-2q>-10). Multiplying by a negative number reverses the inequality sign. While multiplying by (-2), changing the direction is necessary.
Step 3
Exam Tip
ऋणात्मक संख्या से गुणा करने पर असमानता का चिह्न पलटता है। (-2) से गुणा करते समय दिशा बदलना जरूरी है।
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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
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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 \(x-5\ge 1\) का सही हल कौन सा है?
Which is the correct solution of \(x-5\ge 1\)?
#linear inequalities
#solve
#greater equal
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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 (3x<21) का हल क्या है?
What is the solution of (3x<21)?
#linear inequalities
#division positive
#solve
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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 \(-5x\ge 15\) का सही हल क्या है?
What is the correct solution of \(-5x\ge 15\)?
#linear inequalities
#negative division
#solve
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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
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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कौन सा मान \(2x+3\le 11\) को संतुष्ट करता है?
Which value satisfies \(2x+3\le 11\)?
#linear inequalities
#solution check
#two step
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A (x=5)
B (x=6)
C (x=4)
D (x=8)
Explanation opens after your attempt
Step 1
Concept
For (x=4), \(2\cdot4+3=11\), and \(11\le 11\) is true. A sign with equality accepts the boundary value.
Step 2
Why this answer is correct
The correct answer is C. (x=4). For (x=4), \(2\cdot4+3=11\), and \(11\le 11\) is true. A sign with equality accepts the boundary value.
Step 3
Exam Tip
(x=4) रखने पर \(2\cdot4+3=11\) और \(11\le 11\) सत्य है। बराबरी वाला चिह्न सीमा मान को स्वीकार करता है।
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कौन सा मान (4x-2>10) को संतुष्ट करता है?
Which value satisfies (4x-2>10)?
#linear inequalities
#strict inequality
#solution check
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A (x=2)
B (x=3)
C (x=4)
D (x=1)
Explanation opens after your attempt
Step 1
Concept
For (x=4), \(4\cdot4-2=14\), and (14>10) is true. A strict inequality does not include the boundary value.
Step 2
Why this answer is correct
The correct answer is C. (x=4). For (x=4), \(4\cdot4-2=14\), and (14>10) is true. A strict inequality does not include the boundary value.
Step 3
Exam Tip
(x=4) रखने पर \(4\cdot4-2=14\) और (14>10) सत्य है। सख्त असमानता में सीमा मान नहीं चलता।
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असमानता \(x\ge -1\) के लिए संख्या रेखा पर सही रूप कौन सा है?
Which number line form is correct for \(x\ge -1\)?
#linear inequalities
#number line
#closed circle
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A (-1) पर खुला बिंदु और बाईं ओर / Open circle at (-1) and left side
B (-1) पर बंद बिंदु और दाईं ओर / Closed circle at (-1) and right side
C (-1) पर खुला बिंदु और दाईं ओर / Open circle at (-1) and right side
D (-1) पर बंद बिंदु और बाईं ओर / Closed circle at (-1) and left side
Explanation opens after your attempt
Correct Answer
B. (-1) पर बंद बिंदु और दाईं ओर / Closed circle at (-1) and right side
Step 1
Concept
The sign \(\ge\) includes the boundary, and greater numbers are to the right. So use a closed circle at (-1) and shade right.
Step 2
Why this answer is correct
The correct answer is B. (-1) पर बंद बिंदु और दाईं ओर / Closed circle at (-1) and right side. The sign \(\ge\) includes the boundary, and greater numbers are to the right. So use a closed circle at (-1) and shade right.
Step 3
Exam Tip
\(\ge\) में सीमा शामिल होती है और बड़ी संख्याएँ दाईं ओर होती हैं। इसलिए (-1) पर बंद बिंदु और दाईं ओर रेखा बनेगी।
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अंतराल (\(-\infty,9]\) किस असमानता को दर्शाता है?
Which inequality is represented by the interval (\(-\infty,9]\)?
#linear inequalities
#interval notation
#closed endpoint
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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. The interval (\(-\infty,9]\) means \(x\le 9\).
Step 2
Why this answer is correct
The correct answer is B. \(x\le 9\). The square bracket (]) shows that (9) is included. The interval (\(-\infty,9]\) means \(x\le 9\).
Step 3
Exam Tip
वर्ग कोष्ठक (]) बताता है कि (9) शामिल है। (\(-\infty,9]\) का अर्थ \(x\le 9\) है।
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अंतराल (\(4,\infty\)) का असमानता रूप क्या है?
What is the inequality form of the interval (\(4,\infty\))?
#linear inequalities
#interval notation
#open endpoint
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A \(x\ge 4\)
B (x>4)
C (x<4)
D \(x\le 4\)
Explanation opens after your attempt
Step 1
Concept
The parenthesis shows that (4) is not included, and the values lie to the right. Therefore (x>4) is correct.
Step 2
Why this answer is correct
The correct answer is B. (x>4). The parenthesis shows that (4) is not included, and the values lie to the right. Therefore (x>4) is correct.
Step 3
Exam Tip
गोल कोष्ठक बताता है कि (4) शामिल नहीं है और मान दाईं ओर हैं। इसलिए (x>4) सही है।
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असमानता \(1\le x\le 5\) में कौन सा मान शामिल नहीं है?
Which value is not included in \(1\le x\le 5\)?
#linear inequalities
#closed interval
#solution set
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A (1)
B (3)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The number (6) is greater than (5), so it is not included. The sign \(\le\) includes boundaries but not outside values.
Step 2
Why this answer is correct
The correct answer is D. (6). The number (6) is greater than (5), so it is not included. The sign \(\le\) includes boundaries but not outside values.
Step 3
Exam Tip
(6) संख्या (5) से बड़ी है इसलिए शामिल नहीं है। \(\le\) सीमा को शामिल करता है लेकिन उसके बाहर के मान नहीं।
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यदि \(r\le 0\) है तो इनमें से कौन सा मान संभव है?
If \(r\le 0\), which of the following values is possible?
#linear inequalities
#possible value
#boundary
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A (2)
B (5)
C (0)
D (7)
Explanation opens after your attempt
Step 1
Concept
In \(r\le 0\), (0) and smaller numbers are included. With an equality sign, the boundary value is also a solution.
Step 2
Why this answer is correct
The correct answer is C. (0). In \(r\le 0\), (0) and smaller numbers are included. With an equality sign, the boundary value is also a solution.
Step 3
Exam Tip
\(r\le 0\) में (0) और उससे छोटी संख्याएँ शामिल हैं। बराबरी वाले चिह्न में सीमा मान भी हल होता है।
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परीक्षा में छात्र को कम से कम (33) अंक चाहिए। यदि अंक (m) हैं तो सही असमानता क्या है?
A student needs at least (33) marks in an exam. If the marks are (m), what is the correct inequality?
#linear inequalities
#word problem
#at least
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A (m>33)
B \(m\ge 33\)
C (m<33)
D \(m\le 33\)
Explanation opens after your attempt
Correct Answer
B. \(m\ge 33\)
Step 1
Concept
At least (33) means (33) or more. Therefore the correct form is \(m\ge 33\).
Step 2
Why this answer is correct
The correct answer is B. \(m\ge 33\). At least (33) means (33) or more. Therefore the correct form is \(m\ge 33\).
Step 3
Exam Tip
कम से कम (33) का अर्थ (33) या उससे अधिक है। इसलिए सही रूप \(m\ge 33\) है।
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एक डिब्बे का भार (20) किलोग्राम से अधिक नहीं होना चाहिए। यदि भार (w) है तो असमानता क्या होगी?
The weight of a box should not be more than (20) kilograms. If the weight is (w), what is the inequality?
#linear inequalities
#word problem
#maximum
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A (w<20)
B \(w\le 20\)
C (w>20)
D \(w\ge 20\)
Explanation opens after your attempt
Correct Answer
B. \(w\le 20\)
Step 1
Concept
Not more than means at most (20), so \(w\le 20\). The word maximum includes equality.
Step 2
Why this answer is correct
The correct answer is B. \(w\le 20\). Not more than means at most (20), so \(w\le 20\). The word maximum includes equality.
Step 3
Exam Tip
अधिक नहीं का अर्थ अधिकतम (20) है इसलिए \(w\le 20\)। अधिकतम वाले शब्द में बराबरी शामिल होती है।
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किसी पुस्तक की कीमत (250) रुपये से कम है। यदि कीमत (p) है तो सही असमानता क्या है?
The price of a book is less than (250) rupees. If the price is (p), what is the correct inequality?
#linear inequalities
#word problem
#less than
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A (p<250)
B \(p\le 250\)
C (p>250)
D \(p\ge 250\)
Explanation opens after your attempt
Correct Answer
A. (p<250)
Step 1
Concept
Less than means strictly smaller, so (p<250). If equality is included, we write \(\le\).
Step 2
Why this answer is correct
The correct answer is A. (p<250). Less than means strictly smaller, so (p<250). If equality is included, we write \(\le\).
Step 3
Exam Tip
से कम का अर्थ सख्त रूप से कम है इसलिए (p<250)। अगर बराबर शामिल हो तो \(\le\) लिखा जाता है।
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एक प्रतियोगिता में आयु (16) वर्ष से कम नहीं होनी चाहिए। यदि आयु (a) है तो सही असमानता कौन सी है?
In a competition, age must not be less than (16) years. If age is (a), which inequality is correct?
#linear inequalities
#word problem
#not less than
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A (a<16)
B \(a\le 16\)
C \(a\ge 16\)
D (a>16)
Explanation opens after your attempt
Correct Answer
C. \(a\ge 16\)
Step 1
Concept
Not less than means at least (16), so \(a\ge 16\). Do not miss equality in such sentences.
Step 2
Why this answer is correct
The correct answer is C. \(a\ge 16\). Not less than means at least (16), so \(a\ge 16\). Do not miss equality in such sentences.
Step 3
Exam Tip
कम नहीं का अर्थ कम से कम (16) है इसलिए \(a\ge 16\)। ऐसे वाक्यों में बराबरी को न छोड़ें।
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यदि (x=7) है तो कौन सी असमानता सत्य है?
If (x=7), which inequality is true?
#linear inequalities
#substitution
#true option
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A (x<5)
B \(x\le 6\)
C (x>4)
D (x=5)
Explanation opens after your attempt
Step 1
Concept
(7>4) is true, so (x>4) is correct. Substitute the given value in each option.
Step 2
Why this answer is correct
The correct answer is C. (x>4). (7>4) is true, so (x>4) is correct. Substitute the given value in each option.
Step 3
Exam Tip
(7>4) सत्य है इसलिए (x>4) सही है। दिए गए मान को हर विकल्प में रखकर जाँचें।
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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
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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 (8-x<3) का सही हल क्या है?
What is the correct solution of (8-x<3)?
#linear inequalities
#negative coefficient
#solve
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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 \(6x+4\le 22\) का हल कौन सा है?
Which is the solution of \(6x+4\le 22\)?
#linear inequalities
#two step
#solve
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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 \(10-2x\ge 4\) का सही हल क्या है?
What is the correct solution of \(10-2x\ge 4\)?
#linear inequalities
#negative division
#two step
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A \(x\le 3\)
B \(x\ge 3\)
C \(x\le -3\)
D \(x\ge -3\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
From \(10-2x\ge 4\), we get \(-2x\ge -6\), and division by (-2) gives \(x\le 3\). Negative division changes the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). From \(10-2x\ge 4\), we get \(-2x\ge -6\), and division by (-2) gives \(x\le 3\). Negative division changes the direction.
Step 3
Exam Tip
\(10-2x\ge 4\) से \(-2x\ge -6\) और (-2) से भाग देने पर \(x\le 3\)। ऋणात्मक भाग में दिशा बदलती है।
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कौन सा कथन (x<-2) के लिए सही है?
Which statement is correct for (x<-2)?
#linear inequalities
#number line
#strict less
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A समाधान (-2) से दाईं ओर हैं / Solutions are to the right of (-2)
B समाधान (-2) से बाईं ओर हैं और (-2) शामिल नहीं है / Solutions are to the left of (-2) and (-2) is not included
C केवल (x=-2) समाधान है / Only (x=-2) is a solution
D सभी वास्तविक संख्याएँ समाधान हैं / All real numbers are solutions
Explanation opens after your attempt
Correct Answer
B. समाधान (-2) से बाईं ओर हैं और (-2) शामिल नहीं है / Solutions are to the left of (-2) and (-2) is not included
Step 1
Concept
In (x<-2), (-2) is not included and smaller numbers lie to the left. Use an open circle.
Step 2
Why this answer is correct
The correct answer is B. समाधान (-2) से बाईं ओर हैं और (-2) शामिल नहीं है / Solutions are to the left of (-2) and (-2) is not included. In (x<-2), (-2) is not included and smaller numbers lie to the left. Use an open circle.
Step 3
Exam Tip
(x<-2) में (-2) शामिल नहीं है और छोटी संख्याएँ बाईं ओर होती हैं। खुले बिंदु का उपयोग करें।
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असमानता \(x\ge 2\) का अंतराल रूप क्या है?
What is the interval form of \(x\ge 2\)?
#linear inequalities
#interval form
#greater equal
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A (\(2,\infty\))
B \([2,\infty\))
C (\(-\infty,2\))
D (\(-\infty,2]\)
Explanation opens after your attempt
Correct Answer
B. \([2,\infty\))
Step 1
Concept
In \(x\ge 2\), (2) is included and values go to the right. Therefore the interval is \([2,\infty\)).
Step 2
Why this answer is correct
The correct answer is B. \([2,\infty\)). In \(x\ge 2\), (2) is included and values go to the right. Therefore the interval is \([2,\infty\)).
Step 3
Exam Tip
\(x\ge 2\) में (2) शामिल है और मान दाईं ओर जाते हैं। इसलिए अंतराल \([2,\infty\)) है।
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कौन सा विकल्प \(3<x\le 8\) को सही बताता है?
Which option correctly describes \(3<x\le 8\)?
#linear inequalities
#compound inequality
#interpretation
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A (x) (3) से बड़ा और (8) से छोटा या बराबर है / (x) is greater than (3) and less than or equal to (8)
B (x) (3) से छोटा और (8) से बड़ा है / (x) is less than (3) and greater than (8)
C (x) केवल (3) के बराबर है / (x) is only equal to (3)
D (x) केवल (8) से बड़ा है / (x) is only greater than (8)
Explanation opens after your attempt
Correct Answer
A. (x) (3) से बड़ा और (8) से छोटा या बराबर है / (x) is greater than (3) and less than or equal to (8)
Step 1
Concept
In \(3<x\le 8\), (3) is not included but (8) is included. Read a compound inequality from both sides.
Step 2
Why this answer is correct
The correct answer is A. (x) (3) से बड़ा और (8) से छोटा या बराबर है / (x) is greater than (3) and less than or equal to (8). In \(3<x\le 8\), (3) is not included but (8) is included. Read a compound inequality from both sides.
Step 3
Exam Tip
\(3<x\le 8\) में (3) शामिल नहीं है पर (8) शामिल है। संयुक्त असमानता को दोनों तरफ से पढ़ें।
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यदि (x) एक प्राकृतिक संख्या है और \(x\le 5\) है तो संभावित मान कौन से हैं?
If (x) is a natural number and \(x\le 5\), what are the possible values?
#linear inequalities
#natural numbers
#solution set
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A \(x\in{1,2,3,4,5}\)
B \(x\in{0,1,2,3,4,5}\)
C \(x\in{2,3,4,5,6}\)
D \(x\in{1,2,3,4}\)
Explanation opens after your attempt
Correct Answer
A. \(x\in{1,2,3,4,5}\)
Step 1
Concept
Natural numbers are taken from (1), and (5) is included. Therefore \(x\in{1,2,3,4,5}\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\in{1,2,3,4,5}\). Natural numbers are taken from (1), and (5) is included. Therefore \(x\in{1,2,3,4,5}\) is correct.
Step 3
Exam Tip
प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं और (5) शामिल है। इसलिए \(x\in{1,2,3,4,5}\) सही है।
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कौन सी असमानता (n) के अधिकतम (30) होने को दिखाती है?
Which inequality shows that (n) is at most (30)?
#linear inequalities
#at most
#language
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A \(n\le 30\)
B (n<30)
C (n>30)
D \(n\ge 30\)
Explanation opens after your attempt
Correct Answer
A. \(n\le 30\)
Step 1
Concept
At most (30) means (30) or less. Therefore \(n\le 30\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(n\le 30\). At most (30) means (30) or less. Therefore \(n\le 30\) is correct.
Step 3
Exam Tip
अधिकतम (30) का अर्थ (30) या उससे कम है। इसलिए \(n\le 30\) सही है।
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कौन सी असमानता (s) के (12) से अधिक होने को दिखाती है?
Which inequality shows that (s) is more than (12)?
#linear inequalities
#more than
#translation
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A (s<12)
B \(s\le 12\)
C (s>12)
D \(s\ge 12\)
Explanation opens after your attempt
Step 1
Concept
More than means (>), and equality is not included. Therefore (s>12) is correct.
Step 2
Why this answer is correct
The correct answer is C. (s>12). More than means (>), and equality is not included. Therefore (s>12) is correct.
Step 3
Exam Tip
अधिक होने का अर्थ (>) होता है और बराबरी शामिल नहीं होती। इसलिए (s>12) सही है।
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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
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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 \(\frac{x}{4}\le 3\) का हल क्या है?
What is the solution of \(\frac{x}{4}\le 3\)?
#linear inequalities
#fraction
#solve
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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 \(\frac{x}{-3}<2\) का सही हल क्या है?
What is the correct solution of \(\frac{x}{-3}<2\)?
#linear inequalities
#fraction
#negative multiplier
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A (x<-6)
B (x>-6)
C (x<6)
D (x>6)
Explanation opens after your attempt
Step 1
Concept
Multiplying both sides by (-3) reverses the sign, so (x>-6). Negative multiplication changes the direction.
Step 2
Why this answer is correct
The correct answer is B. (x>-6). Multiplying both sides by (-3) reverses the sign, so (x>-6). Negative multiplication changes the direction.
Step 3
Exam Tip
दोनों ओर (-3) से गुणा करने पर चिह्न पलटेगा इसलिए (x>-6)। ऋणात्मक गुणा में दिशा बदलती है।
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असमानता (12<4x) का हल कौन सा है?
Which is the solution of (12<4x)?
#linear inequalities
#solve
#rewrite
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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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किसी कक्षा में विद्यार्थियों की संख्या (n) कम से कम (20) और अधिकतम (45) है। सही असमानता कौन सी है?
In a class, the number of students (n) is at least (20) and at most (45). Which inequality is correct?
#linear inequalities
#word problem
#compound inequality
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A (20<n<45)
B \(20\le n\le 45\)
C \(20\ge n\ge 45\)
D (n<20)
Explanation opens after your attempt
Correct Answer
B. \(20\le n\le 45\)
Step 1
Concept
At least (20) means \(n\ge 20\), and at most (45) means \(n\le 45\). Combining both gives \(20\le n\le 45\).
Step 2
Why this answer is correct
The correct answer is B. \(20\le n\le 45\). At least (20) means \(n\ge 20\), and at most (45) means \(n\le 45\). Combining both gives \(20\le n\le 45\).
Step 3
Exam Tip
कम से कम (20) का अर्थ \(n\ge 20\) और अधिकतम (45) का अर्थ \(n\le 45\) है। दोनों को मिलाकर \(20\le n\le 45\) मिलता है।
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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
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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 (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
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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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यदि (x) पूर्णांक है और \(1<x\le 6\) है तो कुल कितने मान संभव हैं?
If (x) is an integer and \(1<x\le 6\), how many values are possible?
#linear inequalities
#integers
#counting solutions
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The possible integers are (2,3,4,5,6), so there are (5) values. Do not include the endpoint with a strict sign.
Step 2
Why this answer is correct
The correct answer is B. (5). The possible integers are (2,3,4,5,6), so there are (5) values. Do not include the endpoint with a strict sign.
Step 3
Exam Tip
संभव पूर्णांक (2,3,4,5,6) हैं इसलिए कुल (5) मान हैं। सख्त चिह्न वाले किनारे को शामिल न करें।
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इनमें से कौन सी रैखिक असमानता नहीं है?
Which of the following is not a linear inequality?
#linear inequalities
#non linear
#identify
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A \(7-2x\le 5\)
B (3x+1>10)
C \(x^2-4<0\)
D \(9x\ge 18\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-4<0\)
Step 1
Concept
In \(x^2-4<0\), the variable has power (2), so it is not linear. In a linear form, the variable has power (1).
Step 2
Why this answer is correct
The correct answer is C. \(x^2-4<0\). In \(x^2-4<0\), the variable has power (2), so it is not linear. In a linear form, the variable has power (1).
Step 3
Exam Tip
\(x^2-4<0\) में चर की घात (2) है इसलिए यह रैखिक नहीं है। रैखिक रूप में चर की घात (1) होती है।
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अंतराल ([-4,2)) को असमानता के रूप में कैसे लिखेंगे?
How do we write the interval ([-4,2)) as an inequality?
#linear inequalities
#interval notation
#compound inequality
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A (-4<x<2)
B \(-4\le x<2\)
C \(-4<x\le 2\)
D \(-4\le x\le 2\)
Explanation opens after your attempt
Correct Answer
B. \(-4\le x<2\)
Step 1
Concept
The symbol ([-4) shows that (-4) is included and (2)) shows that (2) is not included. Therefore \(-4\le x<2\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(-4\le x<2\). The symbol ([-4) shows that (-4) is included and (2)) shows that (2) is not included. Therefore \(-4\le x<2\) is correct.
Step 3
Exam Tip
([-4) बताता है कि (-4) शामिल है और (2)) बताता है कि (2) शामिल नहीं है। इसलिए \(-4\le x<2\) सही है।
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वाक्य किसी संख्या का दोगुना कम से कम (18) है को असमानता में कैसे लिखेंगे?
How do we write the sentence twice a number is at least (18) as an inequality?
#linear inequalities
#translation
#at least
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A (2x>18)
B \(2x\ge 18\)
C (2x<18)
D \(2x\le 18\)
Explanation opens after your attempt
Correct Answer
B. \(2x\ge 18\)
Step 1
Concept
At least (18) means (18) or more, so \(2x\ge 18\). Connect the phrase at least with \(\ge\).
Step 2
Why this answer is correct
The correct answer is B. \(2x\ge 18\). At least (18) means (18) or more, so \(2x\ge 18\). Connect the phrase at least with \(\ge\).
Step 3
Exam Tip
कम से कम (18) का अर्थ (18) या उससे अधिक है इसलिए \(2x\ge 18\)। शब्द कम से कम को \(\ge\) से जोड़ें।
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असमानता \(\frac{x}{5}>-1\) का हल क्या है?
What is the solution of the inequality \(\frac{x}{5}>-1\)?
#linear inequalities
#fraction
#positive multiplication
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A (x>-5)
B (x<-5)
C (x>5)
D (x<5)
Explanation opens after your attempt
Step 1
Concept
Multiplying both sides by (5) gives (x>-5). Positive multiplication does not change the inequality direction.
Step 2
Why this answer is correct
The correct answer is A. (x>-5). Multiplying both sides by (5) gives (x>-5). Positive multiplication does not change the inequality direction.
Step 3
Exam Tip
दोनों ओर (5) से गुणा करने पर (x>-5) मिलता है। धनात्मक गुणा में असमानता की दिशा नहीं बदलती।
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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
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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
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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यदि \(x\le 2\) है तो दोनों ओर (-3) से गुणा करने पर कौन सा कथन सही होगा?
If \(x\le 2\), which statement is correct after multiplying both sides by (-3)?
#linear inequalities
#negative multiplication
#sign reversal
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A \(-3x\le -6\)
B \(-3x\ge -6\)
C \(3x\le -6\)
D \(-3x\ge 6\)
Explanation opens after your attempt
Correct Answer
B. \(-3x\ge -6\)
Step 1
Concept
Multiplying by the negative number (-3) reverses the inequality sign. Therefore \(-3x\ge -6\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(-3x\ge -6\). Multiplying by the negative number (-3) reverses the inequality sign. Therefore \(-3x\ge -6\) is correct.
Step 3
Exam Tip
ऋणात्मक संख्या (-3) से गुणा करने पर असमानता का चिह्न पलटता है। इसलिए \(-3x\ge -6\) सही है।
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