असमानता (3x+5>14) का हल कौन सा है?
What is the solution of the inequality (3x+5>14)?
#linear inequalities
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A (x>3)
B (x<3)
C \(x\geq 3\)
D \(x\leq 3\)
Explanation opens after your attempt
Step 1
Concept
From (3x>9), we get (x>3). In exams, subtracting the same number from both sides keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x>3). From (3x>9), we get (x>3). In exams, subtracting the same number from both sides keeps the sign unchanged.
Step 3
Exam Tip
(3x>9) से (x>3) मिलता है। परीक्षा में दोनों पक्षों से समान संख्या घटाना सुरक्षित रहता है।
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असमानता \(2x-7\leq 9\) का हल चुनिए।
Choose the solution of the inequality \(2x-7\leq 9\).
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A \(x\leq 8\)
B \(x\geq 8\)
C (x<8)
D (x>8)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 8\)
Step 1
Concept
Since \(2x\leq 16\), \(x\leq 8\). In \(\leq\), the boundary value is included.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 8\). Since \(2x\leq 16\), \(x\leq 8\). In \(\leq\), the boundary value is included.
Step 3
Exam Tip
\(2x\leq 16\) इसलिए \(x\leq 8\) है। \(\leq\) में सीमा भी हल में शामिल होती है।
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यदि (-4x<20), तो सही हल क्या होगा?
If (-4x<20), what is the correct solution?
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A (x>-5)
B (x<-5)
C (x>5)
D (x<5)
Explanation opens after your attempt
Step 1
Concept
Dividing by the negative number (-4) reverses the inequality sign. Hence (x>-5) is correct.
Step 2
Why this answer is correct
The correct answer is A. (x>-5). Dividing by the negative number (-4) reverses the inequality sign. Hence (x>-5) is correct.
Step 3
Exam Tip
ऋणात्मक संख्या (-4) से भाग देने पर असमानता का चिन्ह बदलता है। इसलिए (x>-5) सही है।
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अंतराल ((2,7]) को असमानता के रूप में कैसे लिखेंगे?
How will the interval ((2,7]) be written as an inequality?
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A \(2<x\leq 7\)
B \(2\leq x<7\)
C (2<x<7)
D \(2\leq x\leq 7\)
Explanation opens after your attempt
Correct Answer
A. \(2<x\leq 7\)
Step 1
Concept
In ((2,7]), (2) is not included and (7) is included. Identify open and closed brackets carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2<x\leq 7\). In ((2,7]), (2) is not included and (7) is included. Identify open and closed brackets carefully.
Step 3
Exam Tip
((2,7]) में (2) शामिल नहीं और (7) शामिल है। खुले और बंद कोष्ठक को ध्यान से पहचानें।
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असमानता \(x-4\geq 6\) का हल समुच्चय क्या है?
What is the solution set of \(x-4\geq 6\)?
#linear inequalities
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A \([10,\infty\))
B (\(10,\infty\))
C (\(-\infty,10]\)
D (\(-\infty,10\))
Explanation opens after your attempt
Correct Answer
A. \([10,\infty\))
Step 1
Concept
We get \(x\geq 10\), so the interval is \([10,\infty\)). With \(\geq\), (10) is included.
Step 2
Why this answer is correct
The correct answer is A. \([10,\infty\)). We get \(x\geq 10\), so the interval is \([10,\infty\)). With \(\geq\), (10) is included.
Step 3
Exam Tip
\(x\geq 10\) मिलता है, इसलिए अंतराल \([10,\infty\)) है। \(\geq\) होने पर (10) शामिल रहेगा।
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असमानता \(5-2x\geq 1\) को हल कीजिए।
Solve the inequality \(5-2x\geq 1\).
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A \(x\leq 2\)
B \(x\geq 2\)
C (x<2)
D (x>2)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 2\)
Step 1
Concept
\(-2x\geq -4\), and dividing by a negative gives \(x\leq 2\). Reversing the sign is the key step here.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 2\). \(-2x\geq -4\), and dividing by a negative gives \(x\leq 2\). Reversing the sign is the key step here.
Step 3
Exam Tip
\(-2x\geq -4\) और ऋणात्मक से भाग देने पर \(x\leq 2\) मिलता है। ऐसे प्रश्नों में चिन्ह पलटना सबसे महत्वपूर्ण है।
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कौन सा मान (2x+1<9) का हल नहीं है?
Which value is not a solution of (2x+1<9)?
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A (x=4)
B (x=0)
C (x=-2)
D (x=3)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x<4), so (x=4) is not included. In a strict inequality, the boundary value is not a solution.
Step 2
Why this answer is correct
The correct answer is A. (x=4). The inequality gives (x<4), so (x=4) is not included. In a strict inequality, the boundary value is not a solution.
Step 3
Exam Tip
असमानता से (x<4) मिलता है, इसलिए (x=4) शामिल नहीं है। कठोर असमानता में सीमा मान हल नहीं होता।
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यदि \(x\in\mathbb{N}\) और (x<5), तो हल समुच्चय क्या होगा?
If \(x\in\mathbb{N}\) and (x<5), what is the solution set?
#linear inequalities
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A ({1,2,3,4})
B ({0,1,2,3,4})
C ({1,2,3,4,5})
D (\(-\infty,5\))
Explanation opens after your attempt
Correct Answer
A. ({1,2,3,4})
Step 1
Concept
Usually, \(\mathbb{N}\) means \(1,2,3,\ldots\). Thus the natural numbers less than (5) are ({1,2,3,4}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3,4}). Usually, \(\mathbb{N}\) means \(1,2,3,\ldots\). Thus the natural numbers less than (5) are ({1,2,3,4}).
Step 3
Exam Tip
\(\mathbb{N}\) में सामान्यतः \(1,2,3,\ldots\) लिए जाते हैं। इसलिए (5) से छोटे प्राकृतिक मान ({1,2,3,4}) हैं।
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असमानता \(7x+3\geq 3x+15\) का हल क्या है?
What is the solution of \(7x+3\geq 3x+15\)?
#linear inequalities
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A \(x\geq 3\)
B \(x\leq 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 3\)
Step 1
Concept
From \(4x\geq 12\), we get \(x\geq 3\). Bringing variable terms to one side is a simple method.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 3\). From \(4x\geq 12\), we get \(x\geq 3\). Bringing variable terms to one side is a simple method.
Step 3
Exam Tip
\(4x\geq 12\) से \(x\geq 3\) मिलता है। चर वाले पदों को एक तरफ लाना सरल तरीका है।
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असमानता \(\frac{x}{3}+2<5\) का हल कौन सा है?
Which is the solution of \(\frac{x}{3}+2<5\)?
#linear inequalities
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A (x<9)
B (x>9)
C \(x\leq 9\)
D \(x\geq 9\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{x}{3}<3\), so (x<9). Multiplying by positive (3) does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<9). \(\frac{x}{3}<3\), so (x<9). Multiplying by positive (3) does not change the sign.
Step 3
Exam Tip
\(\frac{x}{3}<3\) इसलिए (x<9) है। धनात्मक (3) से गुणा करने पर चिन्ह नहीं बदलता।
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यदि \(\frac{x-1}{2}\geq 4\), तो (x) का न्यूनतम पूर्णांक मान क्या है?
If \(\frac{x-1}{2}\geq 4\), what is the least integer value of (x)?
#linear inequalities
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A (9)
B (8)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{x-1}{2}\geq 4\), we get \(x\geq 9\). Hence the least integer is (9).
Step 2
Why this answer is correct
The correct answer is A. (9). From \(\frac{x-1}{2}\geq 4\), we get \(x\geq 9\). Hence the least integer is (9).
Step 3
Exam Tip
\(\frac{x-1}{2}\geq 4\) से \(x\geq 9\) मिलता है। इसलिए न्यूनतम पूर्णांक (9) है।
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किस असमानता का हल (\(-\infty,6\)) है?
Which inequality has the solution (\(-\infty,6\))?
#linear inequalities
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A (x<6)
B \(x\leq 6\)
C (x>6)
D \(x\geq 6\)
Explanation opens after your attempt
Step 1
Concept
(\(-\infty,6\)) means all real values less than (6). Since (6) is not included, (x<6) is correct.
Step 2
Why this answer is correct
The correct answer is A. (x<6). (\(-\infty,6\)) means all real values less than (6). Since (6) is not included, (x<6) is correct.
Step 3
Exam Tip
(\(-\infty,6\)) का अर्थ (6) से छोटे सभी वास्तविक मान हैं। (6) शामिल नहीं है, इसलिए (x<6) सही है।
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संयुक्त असमानता \(1<2x+3\leq 11\) का हल क्या है?
What is the solution of the compound inequality \(1<2x+3\leq 11\)?
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A \(-1<x\leq 4\)
B \(-1\leq x<4\)
C \(1<x\leq 4\)
D \(-4<x\leq 1\)
Explanation opens after your attempt
Correct Answer
A. \(-1<x\leq 4\)
Step 1
Concept
Subtracting (3) from all parts gives \(-2<2x\leq 8\), so \(-1<x\leq 4\). Handle both bounds together in compound inequalities.
Step 2
Why this answer is correct
The correct answer is A. \(-1<x\leq 4\). Subtracting (3) from all parts gives \(-2<2x\leq 8\), so \(-1<x\leq 4\). Handle both bounds together in compound inequalities.
Step 3
Exam Tip
सभी भागों से (3) घटाने पर \(-2<2x\leq 8\), इसलिए \(-1<x\leq 4\)। संयुक्त असमानता में दोनों सीमाएं साथ संभालें।
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असमानता \(-3\leq x+2<8\) को हल कीजिए।
Solve the inequality \(-3\leq x+2<8\).
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A \(-5\leq x<6\)
B \(-1\leq x<10\)
C \(-5<x\leq 6\)
D \(-6\leq x<5\)
Explanation opens after your attempt
Correct Answer
A. \(-5\leq x<6\)
Step 1
Concept
Subtracting (2) from all parts gives \(-5\leq x<6\). The equality sign remains on the same boundary.
Step 2
Why this answer is correct
The correct answer is A. \(-5\leq x<6\). Subtracting (2) from all parts gives \(-5\leq x<6\). The equality sign remains on the same boundary.
Step 3
Exam Tip
सभी भागों से (2) घटाने पर \(-5\leq x<6\) मिलता है। बराबरी वाला चिन्ह उसी तरफ बना रहता है।
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कौन सा अंतराल \(x\geq -2\) को दर्शाता है?
Which interval represents \(x\geq -2\)?
#linear inequalities
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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 \(x\geq -2\), (-2) is included and values go to the right. So \([-2,\infty\)) is correct.
Step 2
Why this answer is correct
The correct answer is A. \([-2,\infty\)). In \(x\geq -2\), (-2) is included and values go to the right. So \([-2,\infty\)) is correct.
Step 3
Exam Tip
\(x\geq -2\) में (-2) शामिल है और मान दाईं ओर जाते हैं। इसलिए \([-2,\infty\)) सही है।
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असमानता (4x-5<2x+7) का हल क्या है?
What is the solution of (4x-5<2x+7)?
#linear inequalities
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A (x<6)
B (x>6)
C \(x\leq 6\)
D \(x\geq 6\)
Explanation opens after your attempt
Step 1
Concept
From (2x<12), we get (x<6). Combine like terms to form a simple linear inequality.
Step 2
Why this answer is correct
The correct answer is A. (x<6). From (2x<12), we get (x<6). Combine like terms to form a simple linear inequality.
Step 3
Exam Tip
(2x<12) से (x<6) मिलता है। समान पदों को मिलाकर सरल रैखिक असमानता बनाएं।
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यदि (x) वास्तविक संख्या है, तो \(x^2\geq 0\) किस प्रकार का कथन है?
If (x) is a real number, what type of statement is \(x^2\geq 0\)?
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A हमेशा सत्य / Always true
B हमेशा असत्य / Always false
C केवल (x>0) पर सत्य / True only for (x>0)
D केवल (x<0) पर सत्य / True only for (x<0)
Explanation opens after your attempt
Correct Answer
A. हमेशा सत्य / Always true
Step 1
Concept
The square of any real number is never negative. This is a basic inequality concept.
Step 2
Why this answer is correct
The correct answer is A. हमेशा सत्य / Always true. The square of any real number is never negative. This is a basic inequality concept.
Step 3
Exam Tip
किसी भी वास्तविक संख्या का वर्ग ऋणात्मक नहीं होता। यह मूलभूत असमानता अवधारणा है।
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कौन सा चिह्न कठोर असमानता को दर्शाता है?
Which symbol represents a strict inequality?
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A
B \(\leq\)
C \(\geq\)
D
Explanation opens after your attempt
Step 1
Concept
(<) and (>) are strict inequalities because equality is not included. \(\leq\) and \(\geq\) include equality.
Step 2
Why this answer is correct
The correct answer is A. . (<) and (>) are strict inequalities because equality is not included. \(\leq\) and \(\geq\) include equality.
Step 3
Exam Tip
(<) और (>) कठोर असमानताएं हैं क्योंकि बराबरी शामिल नहीं होती। \(\leq\) और \(\geq\) में बराबरी शामिल होती है।
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असमानता \(6x+1\leq 2x+17\) का सबसे बड़ा पूर्णांक हल क्या है?
What is the greatest integer solution of \(6x+1\leq 2x+17\)?
#linear inequalities
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A (4)
B (5)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
From \(4x\leq 16\), we get \(x\leq 4\). Hence the greatest integer solution is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). From \(4x\leq 16\), we get \(x\leq 4\). Hence the greatest integer solution is (4).
Step 3
Exam Tip
\(4x\leq 16\) से \(x\leq 4\) मिलता है। इसलिए सबसे बड़ा पूर्णांक हल (4) है।
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असमानता (3(x-2)>12) का हल क्या होगा?
What will be the solution of (3(x-2)>12)?
#linear inequalities
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A (x>6)
B (x<6)
C (x>4)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
From (x-2>4), we get (x>6). Expanding brackets or dividing by positive (3) both work.
Step 2
Why this answer is correct
The correct answer is A. (x>6). From (x-2>4), we get (x>6). Expanding brackets or dividing by positive (3) both work.
Step 3
Exam Tip
(x-2>4) से (x>6) मिलता है। पहले कोष्ठक खोलना या धनात्मक (3) से भाग देना दोनों सही हैं।
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असमानता (2(3x+1)\geq 4x+10) का हल चुनिए।
Choose the solution of (2(3x+1)\geq 4x+10).
#linear inequalities
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A \(x\geq 4\)
B \(x\leq 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 4\)
Step 1
Concept
\(6x+2\geq 4x+10\) gives \(2x\geq 8\), so \(x\geq 4\). Multiply every term while opening brackets.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 4\). \(6x+2\geq 4x+10\) gives \(2x\geq 8\), so \(x\geq 4\). Multiply every term while opening brackets.
Step 3
Exam Tip
\(6x+2\geq 4x+10\) से \(2x\geq 8\), इसलिए \(x\geq 4\)। कोष्ठक खोलते समय हर पद पर गुणा करें।
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किस स्थिति में असमानता का चिन्ह उलट जाता है?
In which situation does the inequality sign reverse?
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A दोनों पक्षों को ऋणात्मक संख्या से गुणा करने पर / When both sides are multiplied by a negative number
B दोनों पक्षों में समान संख्या जोड़ने पर / When the same number is added to both sides
C दोनों पक्षों से समान संख्या घटाने पर / When the same number is subtracted from both sides
D दोनों पक्षों को धनात्मक संख्या से भाग देने पर / When both sides are divided by a positive number
Explanation opens after your attempt
Correct Answer
A. दोनों पक्षों को ऋणात्मक संख्या से गुणा करने पर / When both sides are multiplied by a negative number
Step 1
Concept
Multiplying or dividing by a negative number reverses the inequality direction. This is the most common mistake in linear inequalities.
Step 2
Why this answer is correct
The correct answer is A. दोनों पक्षों को ऋणात्मक संख्या से गुणा करने पर / When both sides are multiplied by a negative number. Multiplying or dividing by a negative number reverses the inequality direction. This is the most common mistake in linear inequalities.
Step 3
Exam Tip
ऋणात्मक संख्या से गुणा या भाग करने पर असमानता की दिशा बदलती है। यह रैखिक असमानताओं में सबसे सामान्य गलती है।
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यदि (a>b) और (c<0), तो कौन सा निष्कर्ष सही है?
If (a>b) and (c<0), which conclusion is correct?
#linear inequalities
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A (ac<bc)
B (ac>bc)
C (ac=bc)
D (a+c<b+c)
Explanation opens after your attempt
Correct Answer
A. (ac<bc)
Step 1
Concept
Multiplying by negative (c) changes (>) to (<). Therefore (ac<bc) is correct.
Step 2
Why this answer is correct
The correct answer is A. (ac<bc). Multiplying by negative (c) changes (>) to (<). Therefore (ac<bc) is correct.
Step 3
Exam Tip
ऋणात्मक (c) से गुणा करने पर (>) बदलकर (<) हो जाता है। इसलिए (ac<bc) सही है।
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कौन सा मान असमानता \(-2<x\leq 3\) को संतुष्ट करता है?
Which value satisfies the inequality \(-2<x\leq 3\)?
#linear inequalities
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A (x=3)
B (x=-2)
C (x=4)
D (x=-3)
Explanation opens after your attempt
Step 1
Concept
(-2) is not included, but (3) is included. Hence (x=3) is a correct value.
Step 2
Why this answer is correct
The correct answer is A. (x=3). (-2) is not included, but (3) is included. Hence (x=3) is a correct value.
Step 3
Exam Tip
(-2) शामिल नहीं है लेकिन (3) शामिल है। इसलिए (x=3) सही मान है।
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असमानता (9-3x<0) का हल क्या है?
What is the solution of (9-3x<0)?
#linear inequalities
#introduction
#class 11
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A (x>3)
B (x<3)
C \(x\geq 3\)
D \(x\leq 3\)
Explanation opens after your attempt
Step 1
Concept
(-3x<-9), and dividing by (-3) gives (x>3). Always reverse the sign when dividing by a negative.
Step 2
Why this answer is correct
The correct answer is A. (x>3). (-3x<-9), and dividing by (-3) gives (x>3). Always reverse the sign when dividing by a negative.
Step 3
Exam Tip
(-3x<-9) और (-3) से भाग देने पर (x>3) मिलता है। ऋणात्मक भाग में चिन्ह जरूर उलटें।
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कौन सा अंतराल (x< -1) को सही दर्शाता है?
Which interval correctly represents (x<-1)?
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A (\(-\infty,-1\))
B (\(-\infty,-1]\)
C \([-1,\infty\))
D (\(-1,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,-1\))
Step 1
Concept
In (x<-1), (-1) is not included and all smaller values are included. Hence the open bracket is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-1\)). In (x<-1), (-1) is not included and all smaller values are included. Hence the open bracket is correct.
Step 3
Exam Tip
(x<-1) में (-1) शामिल नहीं है और सभी छोटे मान शामिल हैं। इसलिए खुला कोष्ठक सही है।
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यदि (2x+3>11) और \(x\in\mathbb{Z}\), तो सबसे छोटा पूर्णांक हल कौन सा है?
If (2x+3>11) and \(x\in\mathbb{Z}\), what is the smallest integer solution?
#linear inequalities
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A (5)
B (4)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x>4). Among integers, the smallest solution is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). The inequality gives (x>4). Among integers, the smallest solution is (5).
Step 3
Exam Tip
असमानता से (x>4) मिलता है। पूर्णांकों में सबसे छोटा हल (5) है।
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वाक्य (x) का (4) से कम या बराबर होना किस रूप में लिखा जाएगा?
How is the statement (x) is less than or equal to (4) written?
#linear inequalities
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A \(x\leq 4\)
B (x<4)
C \(x\geq 4\)
D (x>4)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 4\)
Step 1
Concept
The symbol \(\leq\) is used for less than or equal to. Translating words into mathematical symbols is an important exam skill.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 4\). The symbol \(\leq\) is used for less than or equal to. Translating words into mathematical symbols is an important exam skill.
Step 3
Exam Tip
कम या बराबर के लिए \(\leq\) चिह्न प्रयोग होता है। शब्दों को गणितीय चिह्नों में बदलना परीक्षा में जरूरी कौशल है।
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किस संख्या रेखा पर (x>2) दिखेगा?
Which number line representation shows (x>2)?
#linear inequalities
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A (2) पर खुला वृत्त और दाईं ओर छाया / Open circle at (2) and shading to the right
B (2) पर बंद वृत्त और दाईं ओर छाया / Closed circle at (2) and shading to the right
C (2) पर खुला वृत्त और बाईं ओर छाया / Open circle at (2) and shading to the left
D (2) पर बंद वृत्त और बाईं ओर छाया / Closed circle at (2) and shading to the left
Explanation opens after your attempt
Correct Answer
A. (2) पर खुला वृत्त और दाईं ओर छाया / Open circle at (2) and shading to the right
Step 1
Concept
In (x>2), (2) is not included and greater values are needed. So an open circle and right-side shading are correct.
Step 2
Why this answer is correct
The correct answer is A. (2) पर खुला वृत्त और दाईं ओर छाया / Open circle at (2) and shading to the right. In (x>2), (2) is not included and greater values are needed. So an open circle and right-side shading are correct.
Step 3
Exam Tip
(x>2) में (2) शामिल नहीं है और उससे बड़े मान चाहिए। इसलिए खुला वृत्त और दाईं ओर छाया सही है।
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असमानता \(8\leq 2x+4\) का हल कौन सा है?
Which is the solution of \(8\leq 2x+4\)?
#linear inequalities
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A \(x\geq 2\)
B \(x\leq 2\)
C (x>2)
D (x<2)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 2\)
Step 1
Concept
From \(4\leq 2x\), we get \(2\leq x\), that is \(x\geq 2\). Pay attention to direction while reading inequalities.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 2\). From \(4\leq 2x\), we get \(2\leq x\), that is \(x\geq 2\). Pay attention to direction while reading inequalities.
Step 3
Exam Tip
\(4\leq 2x\) से \(2\leq x\), अर्थात \(x\geq 2\)। असमानता को पढ़ते समय दिशा का ध्यान रखें।
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असमानता \(\frac{2x+1}{5}\leq 3\) को हल कीजिए।
Solve the inequality \(\frac{2x+1}{5}\leq 3\).
#linear inequalities
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A \(x\leq 7\)
B \(x\geq 7\)
C (x<7)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 7\)
Step 1
Concept
Multiplying by positive (5) gives \(2x+1\leq 15\), so \(x\leq 7\). A positive denominator does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 7\). Multiplying by positive (5) gives \(2x+1\leq 15\), so \(x\leq 7\). A positive denominator does not reverse the sign.
Step 3
Exam Tip
धनात्मक (5) से गुणा करने पर \(2x+1\leq 15\), इसलिए \(x\leq 7\)। धनात्मक हर होने पर चिन्ह नहीं बदलता।
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यदि \(-1\leq x<4\), तो सही अंतराल रूप क्या है?
If \(-1\leq x<4\), what is the correct interval form?
#linear inequalities
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A ([-1,4))
B ((-1,4])
C ((-1,4))
D ([-1,4])
Explanation opens after your attempt
Correct Answer
A. ([-1,4))
Step 1
Concept
(-1) is included, so use a square bracket; (4) is not included, so use a round bracket. Check both endpoints separately while writing intervals.
Step 2
Why this answer is correct
The correct answer is A. ([-1,4)). (-1) is included, so use a square bracket; (4) is not included, so use a round bracket. Check both endpoints separately while writing intervals.
Step 3
Exam Tip
(-1) शामिल है इसलिए वर्ग कोष्ठक और (4) शामिल नहीं है इसलिए गोल कोष्ठक लगेगा। अंतराल लिखते समय दोनों सिरों को अलग जांचें।
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कौन सा विकल्प \(x\leq 0\) का उदाहरण है?
Which option is an example of \(x\leq 0\)?
#linear inequalities
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A (x=-3)
B (x=2)
C (x=5)
D (x=1)
Explanation opens after your attempt
Step 1
Concept
\(x\leq 0\) includes zero and all smaller values. (x=-3) is one such value.
Step 2
Why this answer is correct
The correct answer is A. (x=-3). \(x\leq 0\) includes zero and all smaller values. (x=-3) is one such value.
Step 3
Exam Tip
\(x\leq 0\) में शून्य या उससे छोटे मान आते हैं। (x=-3) ऐसे मानों में से एक है।
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असमानता (10<3x+1) का हल क्या है?
What is the solution of (10<3x+1)?
#linear inequalities
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#class 11
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A (x>3)
B (x<3)
C \(x\geq 3\)
D \(x\leq 3\)
Explanation opens after your attempt
Step 1
Concept
From (9<3x), we get (3<x), meaning (x>3). (3<x) and (x>3) mean the same thing.
Step 2
Why this answer is correct
The correct answer is A. (x>3). From (9<3x), we get (3<x), meaning (x>3). (3<x) and (x>3) mean the same thing.
Step 3
Exam Tip
(9<3x) से (3<x), यानी (x>3) मिलता है। (3<x) और (x>3) समान अर्थ रखते हैं।
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यदि (x+5<12), तो (x) के कौन से पूर्णांक मान \(0\leq x\) के साथ संभव हैं?
If (x+5<12), which integer values of (x) are possible with \(0\leq x\)?
#linear inequalities
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A ({0,1,2,3,4,5,6})
B ({0,1,2,3,4,5,6,7})
C ({1,2,3,4,5,6,7})
D ({0,1,2,3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({0,1,2,3,4,5,6})
Step 1
Concept
(x+5<12) gives (x<7), and \(0\leq x\) is given. So the integer values are ({0,1,2,3,4,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({0,1,2,3,4,5,6}). (x+5<12) gives (x<7), and \(0\leq x\) is given. So the integer values are ({0,1,2,3,4,5,6}).
Step 3
Exam Tip
(x+5<12) से (x<7) और \(0\leq x\) दिया है। इसलिए पूर्णांक मान ({0,1,2,3,4,5,6}) होंगे।
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कौन सा कथन \(x\geq 5\) के बारे में सही है?
Which statement about \(x\geq 5\) is correct?
#linear inequalities
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A (5) हल में शामिल है / (5) is included in the solution
B (5) हल में शामिल नहीं है / (5) is not included in the solution
C केवल (x=5) हल है / Only (x=5) is the solution
D केवल (x<5) हल है / Only (x<5) is the solution
Explanation opens after your attempt
Correct Answer
A. (5) हल में शामिल है / (5) is included in the solution
Step 1
Concept
\(\geq\) means greater than or equal to, so (5) is included. On the number line, use a closed circle at (5).
Step 2
Why this answer is correct
The correct answer is A. (5) हल में शामिल है / (5) is included in the solution. \(\geq\) means greater than or equal to, so (5) is included. On the number line, use a closed circle at (5).
Step 3
Exam Tip
\(\geq\) का अर्थ बड़ा या बराबर होता है, इसलिए (5) शामिल है। संख्या रेखा पर (5) पर बंद वृत्त बनेगा।
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असमानता (3x-2> x+8) का हल चुनिए।
Choose the solution of (3x-2>x+8).
#linear inequalities
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A (x>5)
B (x<5)
C \(x\geq 5\)
D \(x\leq 5\)
Explanation opens after your attempt
Step 1
Concept
From (2x>10), we get (x>5). There is no equality, so (5) will not be included.
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (2x>10), we get (x>5). There is no equality, so (5) will not be included.
Step 3
Exam Tip
(2x>10) से (x>5) मिलता है। बराबरी नहीं है, इसलिए (5) शामिल नहीं होगा।
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यदि (x) एक वास्तविक संख्या है और (x<0), तो (-x) के बारे में क्या सही है?
If (x) is a real number and (x<0), what is true about (-x)?
#linear inequalities
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A (-x>0)
B (-x<0)
C (-x=0)
D \(-x\leq 0\)
Explanation opens after your attempt
Step 1
Concept
The opposite of a negative number is positive. Therefore, if (x<0), then (-x>0).
Step 2
Why this answer is correct
The correct answer is A. (-x>0). The opposite of a negative number is positive. Therefore, if (x<0), then (-x>0).
Step 3
Exam Tip
ऋणात्मक संख्या का विपरीत धनात्मक होता है। इसलिए (x<0) होने पर (-x>0) है।
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असमानता \(2x+5\leq x+9\) में सीमा मान क्या है?
What is the boundary value in the inequality \(2x+5\leq x+9\)?
#linear inequalities
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A (4)
B (5)
C (9)
D (2)
Explanation opens after your attempt
Step 1
Concept
The boundary value is found by using equality: (2x+5=x+9), so (x=4). The boundary value decides the open or closed endpoint.
Step 2
Why this answer is correct
The correct answer is A. (4). The boundary value is found by using equality: (2x+5=x+9), so (x=4). The boundary value decides the open or closed endpoint.
Step 3
Exam Tip
सीमा मान बराबरी लगाकर मिलता है: (2x+5=x+9), इसलिए (x=4)। सीमा मान से खुला या बंद सिरा तय होता है।
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किस असमानता का हल \(x\leq -3\) है?
Which inequality has the solution \(x\leq -3\)?
#linear inequalities
#introduction
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A \(x+3\leq 0\)
B \(x-3\leq 0\)
C \(x+3\geq 0\)
D \(x-3\geq 0\)
Explanation opens after your attempt
Correct Answer
A. \(x+3\leq 0\)
Step 1
Concept
\(x+3\leq 0\) gives \(x\leq -3\). Solving each option and matching is a quick method.
Step 2
Why this answer is correct
The correct answer is A. \(x+3\leq 0\). \(x+3\leq 0\) gives \(x\leq -3\). Solving each option and matching is a quick method.
Step 3
Exam Tip
\(x+3\leq 0\) से \(x\leq -3\) मिलता है। विकल्पों को हल करके मिलान करना तेज तरीका है।
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यदि \(5x\leq -20\), तो सही हल क्या है?
If \(5x\leq -20\), what is the correct solution?
#linear inequalities
#introduction
#class 11
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A \(x\leq -4\)
B \(x\geq -4\)
C (x<-4)
D (x>-4)
Explanation opens after your attempt
Correct Answer
A. \(x\leq -4\)
Step 1
Concept
Dividing by positive (5) does not change the sign. Hence \(x\leq -4\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq -4\). Dividing by positive (5) does not change the sign. Hence \(x\leq -4\) is correct.
Step 3
Exam Tip
धनात्मक (5) से भाग देने पर चिन्ह नहीं बदलता। इसलिए \(x\leq -4\) सही है।
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असमानता \(-5x\geq 15\) को हल कीजिए।
Solve the inequality \(-5x\geq 15\).
#linear inequalities
#introduction
#class 11
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A \(x\leq -3\)
B \(x\geq -3\)
C (x<-3)
D (x>-3)
Explanation opens after your attempt
Correct Answer
A. \(x\leq -3\)
Step 1
Concept
Dividing by (-5) reverses the inequality sign. Therefore \(x\leq -3\) is obtained.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq -3\). Dividing by (-5) reverses the inequality sign. Therefore \(x\leq -3\) is obtained.
Step 3
Exam Tip
(-5) से भाग देने पर असमानता का चिन्ह उलटता है। इसलिए \(x\leq -3\) मिलता है।
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कौन सा विकल्प ({x:x>1}) का अंतराल रूप है?
Which option is the interval form of ({x:x>1})?
#linear inequalities
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A (\(1,\infty\))
B \([1,\infty\))
C (\(-\infty,1\))
D (\(-\infty,1]\)
Explanation opens after your attempt
Correct Answer
A. (\(1,\infty\))
Step 1
Concept
In (x>1), (1) is not included and values to the right are taken. Hence (\(1,\infty\)) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(1,\infty\)). In (x>1), (1) is not included and values to the right are taken. Hence (\(1,\infty\)) is correct.
Step 3
Exam Tip
(x>1) में (1) शामिल नहीं है और दाईं ओर के मान आते हैं। इसलिए (\(1,\infty\)) सही है।
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यदि \(2\leq x\leq 6\), तो निम्न में से कौन सा मान हल है?
If \(2\leq x\leq 6\), which of the following is a solution?
#linear inequalities
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A (x=6)
B (x=7)
C (x=1)
D (x=0)
Explanation opens after your attempt
Step 1
Concept
Both boundaries include equality, so (2) and (6) are included. Among the options, (x=6) is correct.
Step 2
Why this answer is correct
The correct answer is A. (x=6). Both boundaries include equality, so (2) and (6) are included. Among the options, (x=6) is correct.
Step 3
Exam Tip
दोनों सीमाओं में बराबरी है, इसलिए (2) और (6) शामिल हैं। दिए गए विकल्पों में (x=6) सही है।
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असमानता \(4- \frac{x}{2}>1\) का हल क्या है?
What is the solution of \(4-\frac{x}{2}>1\)?
#linear inequalities
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#class 11
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A (x<6)
B (x>6)
C \(x\leq 6\)
D \(x\geq 6\)
Explanation opens after your attempt
Step 1
Concept
\(-\frac{x}{2}>-3\), and removing the negative factor gives (x<6). Identify when the sign must be reversed.
Step 2
Why this answer is correct
The correct answer is A. (x<6). \(-\frac{x}{2}>-3\), and removing the negative factor gives (x<6). Identify when the sign must be reversed.
Step 3
Exam Tip
\(-\frac{x}{2}>-3\) और ऋणात्मक गुणक हटाने पर (x<6) मिलता है। चिन्ह बदलने की स्थिति पहचानें।
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एक संख्या में (3) जोड़ने पर परिणाम (10) से बड़ा है। सही असमानता क्या है?
A number increased by (3) is greater than (10). What is the correct inequality?
#linear inequalities
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A (x+3>10)
B (x+3<10)
C (3x>10)
D (x-3>10)
Explanation opens after your attempt
Correct Answer
A. (x+3>10)
Step 1
Concept
Increasing by (3) means (x+3), and greater than means (>). In word problems, define the variable first.
Step 2
Why this answer is correct
The correct answer is A. (x+3>10). Increasing by (3) means (x+3), and greater than means (>). In word problems, define the variable first.
Step 3
Exam Tip
वाक्य में (3) जोड़ना (x+3) और बड़ा है (>) को दर्शाता है। शब्द आधारित प्रश्नों में पहले चर तय करें।
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असमानता \(7\leq x+4<12\) का हल क्या है?
What is the solution of \(7\leq x+4<12\)?
#linear inequalities
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#class 11
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A \(3\leq x<8\)
B \(3<x\leq 8\)
C \(11\leq x<16\)
D \(2\leq x<7\)
Explanation opens after your attempt
Correct Answer
A. \(3\leq x<8\)
Step 1
Concept
Subtracting (4) from all parts gives \(3\leq x<8\). Apply the same operation to every part of a compound inequality.
Step 2
Why this answer is correct
The correct answer is A. \(3\leq x<8\). Subtracting (4) from all parts gives \(3\leq x<8\). Apply the same operation to every part of a compound inequality.
Step 3
Exam Tip
सभी भागों से (4) घटाने पर \(3\leq x<8\) मिलता है। संयुक्त असमानता में हर भाग पर समान क्रिया करें।
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कौन सा विकल्प \(x\in\mathbb{R}\) और \(x\geq 0\) को दर्शाता है?
Which option represents \(x\in\mathbb{R}\) and \(x\geq 0\)?
#linear inequalities
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A \([0,\infty\))
B (\(0,\infty\))
C (\(-\infty,0\))
D (\(-\infty,0]\)
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Correct Answer
A. \([0,\infty\))
Step 1
Concept
\(x\geq 0\) includes (0) and all positive real numbers. Therefore \([0,\infty\)) is correct.
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). \(x\geq 0\) includes (0) and all positive real numbers. Therefore \([0,\infty\)) is correct.
Step 3
Exam Tip
\(x\geq 0\) में (0) और सभी धनात्मक वास्तविक संख्याएं शामिल हैं। इसलिए \([0,\infty\)) सही है।
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एक विद्यार्थी को परीक्षा पास करने के लिए कम से कम (40) अंक चाहिए। यदि उसे पहले से (27) अंक मिल चुके हैं, तो अतिरिक्त अंकों (m) के लिए सही असमानता क्या है?
A student needs at least (40) marks to pass. If the student already has (27) marks, what is the correct inequality for extra marks (m)?
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A \(27+m\geq 40\)
B (27+m>40)
C \(27-m\geq 40\)
D \(m-27\leq 40\)
Explanation opens after your attempt
Correct Answer
A. \(27+m\geq 40\)
Step 1
Concept
At least means \(\geq\), so \(27+m\geq 40\) is correct. In word problems, first identify the mathematical symbol for the key phrase.
Step 2
Why this answer is correct
The correct answer is A. \(27+m\geq 40\). At least means \(\geq\), so \(27+m\geq 40\) is correct. In word problems, first identify the mathematical symbol for the key phrase.
Step 3
Exam Tip
कम से कम का अर्थ \(\geq\) होता है, इसलिए \(27+m\geq 40\) सही है। शब्द प्रश्नों में पहले मुख्य शब्द का गणितीय चिह्न पहचानें।
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किसी संख्या के (2) गुने में (5) जोड़ने पर परिणाम (19) से अधिक नहीं है। (x) के लिए सही हल क्या है?
Twice a number increased by (5) is not more than (19). What is the correct solution for (x)?
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A \(x\leq 7\)
B \(x\geq 7\)
C (x<7)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 7\)
Step 1
Concept
Not more than means \(\leq\), so \(2x+5\leq 19\) gives \(x\leq 7\). In word problems, first convert the sentence into an inequality.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 7\). Not more than means \(\leq\), so \(2x+5\leq 19\) gives \(x\leq 7\). In word problems, first convert the sentence into an inequality.
Step 3
Exam Tip
अधिक नहीं है का अर्थ \(\leq\) होता है, इसलिए \(2x+5\leq 19\) से \(x\leq 7\) मिलता है। शब्द प्रश्नों में वाक्य को पहले असमानता में बदलें।
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