असमानता (3x-5>10) का हल क्या है?
What is the solution of the inequality (3x-5>10)?
#linear-inequalities
#one-variable
#algebraic-solution
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A (x>5)
B (x<5)
C \(x\geq5\)
D \(x\leq5\)
Explanation opens after your attempt
Step 1
Concept
Adding (5) gives (3x>15) and then (x>5). In exams remember that dividing by a positive number does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Adding (5) gives (3x>15) and then (x>5). In exams remember that dividing by a positive number does not reverse the sign.
Step 3
Exam Tip
(3x-5>10) में (5) जोड़कर (3x>15) और फिर (x>5) मिलता है। परीक्षा में समान धन संख्या से भाग देने पर चिन्ह नहीं बदलता।
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असमानता \(2x+7\leq15\) का हल चुनिए।
Choose the solution of the inequality \(2x+7\leq15\).
#linear-inequalities
#one-variable
#algebraic-solution
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A \(x\leq4\)
B \(x\geq4\)
C (x<4)
D (x>4)
Explanation opens after your attempt
Correct Answer
A. \(x\leq4\)
Step 1
Concept
Subtracting (7) gives \(2x\leq8\) so \(x\leq4\). A closed inequality sign includes equality.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq4\). Subtracting (7) gives \(2x\leq8\) so \(x\leq4\). A closed inequality sign includes equality.
Step 3
Exam Tip
(7) घटाने पर \(2x\leq8\) और इसलिए \(x\leq4\) मिलता है। बंद चिन्ह में बराबरी भी शामिल रहती है।
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असमानता \(5-2x\geq11\) का हल क्या है?
What is the solution of \(5-2x\geq11\)?
#linear-inequalities
#negative-coefficient
#medium
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A \(x\leq-3\)
B \(x\geq-3\)
C \(x\leq3\)
D \(x\geq3\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq-3\)
Step 1
Concept
Subtracting (5) gives \(-2x\geq6\) and dividing by (-2) gives \(x\leq-3\). Do not forget to reverse the sign for a negative coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq-3\). Subtracting (5) gives \(-2x\geq6\) and dividing by (-2) gives \(x\leq-3\). Do not forget to reverse the sign for a negative coefficient.
Step 3
Exam Tip
(5) घटाने पर \(-2x\geq6\) और (-2) से भाग देने पर \(x\leq-3\) मिलता है। ऋण गुणांक पर चिन्ह बदलना न भूलें।
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असमानता \(\frac{x}{3}+2>6\) का हल चुनिए।
Choose the solution of \(\frac{x}{3}+2>6\).
#linear-inequalities
#fraction
#one-variable
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A (x>12)
B (x<12)
C (x>4)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
Subtracting (2) gives \(\frac{x}{3}>4\) and multiplying by (3) gives (x>12). Multiplying by a positive number keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x>12). Subtracting (2) gives \(\frac{x}{3}>4\) and multiplying by (3) gives (x>12). Multiplying by a positive number keeps the sign unchanged.
Step 3
Exam Tip
(2) घटाने पर \(\frac{x}{3}>4\) और (3) से गुणा करने पर (x>12) मिलता है। धन संख्या से गुणा करने पर चिन्ह वही रहता है।
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असमानता \(\frac{x-1}{2}\leq5\) का हल क्या होगा?
What will be the solution of \(\frac{x-1}{2}\leq5\)?
#linear-inequalities
#fraction
#algebraic-solution
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A \(x\leq11\)
B \(x\geq11\)
C \(x\leq9\)
D \(x\geq9\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq11\)
Step 1
Concept
Multiplying by (2) gives \(x-1\leq10\) so \(x\leq11\). Clearing the denominator first makes the solution easier.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq11\). Multiplying by (2) gives \(x-1\leq10\) so \(x\leq11\). Clearing the denominator first makes the solution easier.
Step 3
Exam Tip
(2) से गुणा करने पर \(x-1\leq10\) और इसलिए \(x\leq11\) है। पहले हर हटाना समाधान को आसान बनाता है।
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असमानता \(\frac{2x+3}{5}\geq3\) को हल कीजिए।
Solve the inequality \(\frac{2x+3}{5}\geq3\).
#linear-inequalities
#fraction
#medium
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A \(x\geq6\)
B \(x\leq6\)
C \(x\geq9\)
D \(x\leq9\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq6\)
Step 1
Concept
Multiplying by (5) gives \(2x+3\geq15\) and then \(2x\geq12\) gives \(x\geq6\). A positive denominator does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq6\). Multiplying by (5) gives \(2x+3\geq15\) and then \(2x\geq12\) gives \(x\geq6\). A positive denominator does not reverse the sign.
Step 3
Exam Tip
(5) से गुणा करने पर \(2x+3\geq15\) और फिर \(2x\geq12\) से \(x\geq6\) मिलता है। हर धन हो तो चिन्ह नहीं बदलता।
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असमानता \(\frac{7-3x}{2}< -1\) का हल चुनिए।
Choose the solution of \(\frac{7-3x}{2}< -1\).
#linear-inequalities
#fraction
#negative-coefficient
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A (x>3)
B (x<3)
C (x> -3)
D (x< -3)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (2) gives (7-3x<-2) and (-3x<-9). Dividing by (-3) reverses the sign to (x>3).
Step 2
Why this answer is correct
The correct answer is A. (x>3). Multiplying by (2) gives (7-3x<-2) and (-3x<-9). Dividing by (-3) reverses the sign to (x>3).
Step 3
Exam Tip
(2) से गुणा करने पर (7-3x<-2) और (-3x<-9) मिलता है। (-3) से भाग देने पर चिन्ह बदलकर (x>3) होता है।
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असमानता \(4x-7\leq x+8\) का हल क्या है?
What is the solution of \(4x-7\leq x+8\)?
#linear-inequalities
#variables-both-sides
#medium
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A \(x\leq5\)
B \(x\geq5\)
C (x<5)
D (x>5)
Explanation opens after your attempt
Correct Answer
A. \(x\leq5\)
Step 1
Concept
Bringing like terms together gives \(3x\leq15\) so \(x\leq5\). Keep variable terms on one side carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq5\). Bringing like terms together gives \(3x\leq15\) so \(x\leq5\). Keep variable terms on one side carefully.
Step 3
Exam Tip
समान पदों को एक तरफ लाने पर \(3x\leq15\) मिलता है इसलिए \(x\leq5\) है। चर पदों को एक ही तरफ सावधानी से रखें।
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असमानता (6x+1>2x+13) का हल कौन सा है?
Which is the solution of (6x+1>2x+13)?
#linear-inequalities
#variables-both-sides
#strict
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A (x>3)
B (x<3)
C \(x\geq3\)
D \(x\leq3\)
Explanation opens after your attempt
Step 1
Concept
Removing (2x) and (1) gives (4x>12) so (x>3). A strict sign does not include equality.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Removing (2x) and (1) gives (4x>12) so (x>3). A strict sign does not include equality.
Step 3
Exam Tip
(2x) और (1) हटाने पर (4x>12) मिलता है इसलिए (x>3) है। कठोर चिन्ह में बराबरी शामिल नहीं होती।
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असमानता \(3(x-2)\geq2x+5\) को हल कीजिए।
Solve the inequality \(3(x-2)\geq2x+5\).
#linear-inequalities
#brackets
#one-variable
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A \(x\geq11\)
B \(x\leq11\)
C \(x\geq1\)
D \(x\leq1\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq11\)
Step 1
Concept
Expanding gives \(3x-6\geq2x+5\) and hence \(x\geq11\). Watch the signs while opening brackets.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq11\). Expanding gives \(3x-6\geq2x+5\) and hence \(x\geq11\). Watch the signs while opening brackets.
Step 3
Exam Tip
विस्तार करने पर \(3x-6\geq2x+5\) और इसलिए \(x\geq11\) मिलता है। कोष्ठक खोलते समय चिन्हों का ध्यान रखें।
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असमानता (2(3x+1)<5x+9) का हल क्या है?
What is the solution of (2(3x+1)<5x+9)?
#linear-inequalities
#brackets
#medium
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A (x<7)
B (x>7)
C (x< -7)
D (x> -7)
Explanation opens after your attempt
Step 1
Concept
Expansion gives (6x+2<5x+9) so (x<7). When both sides have variables solve in small steps.
Step 2
Why this answer is correct
The correct answer is A. (x<7). Expansion gives (6x+2<5x+9) so (x<7). When both sides have variables solve in small steps.
Step 3
Exam Tip
विस्तार से (6x+2<5x+9) मिलता है इसलिए (x<7) है। दोनों पक्षों में चर हो तो छोटे चरणों में हल करें।
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असमानता \(5(x+2)-3\leq2x+16\) का हल चुनिए।
Choose the solution of \(5(x+2)-3\leq2x+16\).
#linear-inequalities
#brackets
#simplification
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A \(x\leq3\)
B \(x\geq3\)
C \(x\leq-3\)
D \(x\geq-3\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq3\)
Step 1
Concept
Simplifying gives \(5x+7\leq2x+16\) and \(3x\leq9\). The final answer is \(x\leq3\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq3\). Simplifying gives \(5x+7\leq2x+16\) and \(3x\leq9\). The final answer is \(x\leq3\).
Step 3
Exam Tip
सरल करने पर \(5x+7\leq2x+16\) और \(3x\leq9\) मिलता है। अंतिम उत्तर \(x\leq3\) है।
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असमानता (7-2(1-x)>3x-4) को हल कीजिए।
Solve the inequality (7-2(1-x)>3x-4).
#linear-inequalities
#brackets
#signs
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A (x<9)
B (x>9)
C (x< -9)
D (x> -9)
Explanation opens after your attempt
Step 1
Concept
The left side becomes (5+2x) so (5+2x>3x-4) gives (x<9). Signs change while opening a negative bracket.
Step 2
Why this answer is correct
The correct answer is A. (x<9). The left side becomes (5+2x) so (5+2x>3x-4) gives (x<9). Signs change while opening a negative bracket.
Step 3
Exam Tip
बायां पक्ष (5+2x) बनता है इसलिए (5+2x>3x-4) से (x<9) मिलता है। ऋण कोष्ठक खोलते समय संकेत बदलते हैं।
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युग्म असमानता \(2<x+3\leq8\) का हल क्या है?
What is the solution of the compound inequality \(2<x+3\leq8\)?
#linear-inequalities
#compound-inequality
#interval
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A \(-1<x\leq5\)
B (x<-1)
C \(x\geq5\)
D \(-1\leq x<5\)
Explanation opens after your attempt
Correct Answer
A. \(-1<x\leq5\)
Step 1
Concept
Subtracting (3) from all parts gives \(-1<x\leq5\). In a compound inequality apply the same operation to every part.
Step 2
Why this answer is correct
The correct answer is A. \(-1<x\leq5\). Subtracting (3) from all parts gives \(-1<x\leq5\). In a compound inequality apply the same operation to every part.
Step 3
Exam Tip
तीनों भागों से (3) घटाने पर \(-1<x\leq5\) मिलता है। युग्म असमानता में वही क्रिया सभी भागों पर करें।
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युग्म असमानता \(-4\leq2x+2<10\) का हल चुनिए।
Choose the solution of \(-4\leq2x+2<10\).
#linear-inequalities
#compound-inequality
#medium
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A \(-3\leq x<4\)
B \(-3<x\leq4\)
C \(x\leq-3\)
D (x>4)
Explanation opens after your attempt
Correct Answer
A. \(-3\leq x<4\)
Step 1
Concept
Subtracting (2) from all parts gives \(-6\leq2x<8\) and then \(-3\leq x<4\). Keep open and closed signs correctly.
Step 2
Why this answer is correct
The correct answer is A. \(-3\leq x<4\). Subtracting (2) from all parts gives \(-6\leq2x<8\) and then \(-3\leq x<4\). Keep open and closed signs correctly.
Step 3
Exam Tip
सभी भागों से (2) घटाने पर \(-6\leq2x<8\) और फिर \(-3\leq x<4\) मिलता है। खुले और बंद चिन्ह को जस का तस रखें।
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युग्म असमानता \(1<\frac{x-2}{3}\leq4\) का हल क्या है?
What is the solution of \(1<\frac{x-2}{3}\leq4\)?
#linear-inequalities
#compound-inequality
#fraction
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A \(5<x\leq14\)
B \(5\leq x<14\)
C (x>14)
D \(x\leq5\)
Explanation opens after your attempt
Correct Answer
A. \(5<x\leq14\)
Step 1
Concept
Multiplying by (3) gives \(3<x-2\leq12\) and then \(5<x\leq14\). A positive multiplier does not change the signs.
Step 2
Why this answer is correct
The correct answer is A. \(5<x\leq14\). Multiplying by (3) gives \(3<x-2\leq12\) and then \(5<x\leq14\). A positive multiplier does not change the signs.
Step 3
Exam Tip
(3) से गुणा करने पर \(3<x-2\leq12\) और फिर \(5<x\leq14\) मिलता है। धन गुणक से चिन्ह नहीं बदलता।
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असमानता \(4x+1\geq9\) का अंतराल रूप चुनिए।
Choose the interval form of \(4x+1\geq9\).
#linear-inequalities
#interval-notation
#closed-endpoint
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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
The solution is \(x\geq2\) so the interval is \([2,\infty\)). Use a square bracket when equality is included.
Step 2
Why this answer is correct
The correct answer is A. \([2,\infty\)). The solution is \(x\geq2\) so the interval is \([2,\infty\)). Use a square bracket when equality is included.
Step 3
Exam Tip
हल \(x\geq2\) है इसलिए अंतराल \([2,\infty\)) है। बराबरी शामिल हो तो वर्ग कोष्ठक लगाएं।
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समुच्चय रूप में \(x\leq-1\) का सही निरूपण कौन सा है?
Which is the correct set form for \(x\leq-1\)?
#linear-inequalities
#set-builder
#solution-set
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A \({x:x\in\mathbb{R},x\leq-1}\)
B \({x:x\in\mathbb{R},x<-1}\)
C \({x:x\in\mathbb{R},x\geq-1}\)
D \({x:x\in\mathbb{N},x\leq-1}\)
Explanation opens after your attempt
Correct Answer
A. \({x:x\in\mathbb{R},x\leq-1}\)
Step 1
Concept
The inequality \(x\leq-1\) includes (-1) and all smaller real numbers. For real solutions writing \(\mathbb{R}\) is appropriate.
Step 2
Why this answer is correct
The correct answer is A. \({x:x\in\mathbb{R},x\leq-1}\). The inequality \(x\leq-1\) includes (-1) and all smaller real numbers. For real solutions writing \(\mathbb{R}\) is appropriate.
Step 3
Exam Tip
\(x\leq-1\) में (-1) और उससे छोटी वास्तविक संख्याएं आती हैं। वास्तविक हल के लिए \(\mathbb{R}\) लिखना उचित है।
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असमानता \(9-3x\leq0\) का हल समुच्चय क्या है?
What is the solution set of \(9-3x\leq0\)?
#linear-inequalities
#set-builder
#negative-coefficient
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A \({x:x\in\mathbb{R},x\geq3}\)
B \({x:x\in\mathbb{R},x\leq3}\)
C \({x:x\in\mathbb{R},x>3}\)
D \({x:x\in\mathbb{R},x<3}\)
Explanation opens after your attempt
Correct Answer
A. \({x:x\in\mathbb{R},x\geq3}\)
Step 1
Concept
From \(9-3x\leq0\) we get \(-3x\leq-9\) and then \(x\geq3\). The sign reverses when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \({x:x\in\mathbb{R},x\geq3}\). From \(9-3x\leq0\) we get \(-3x\leq-9\) and then \(x\geq3\). The sign reverses when dividing by a negative number.
Step 3
Exam Tip
\(9-3x\leq0\) से \(-3x\leq-9\) और \(x\geq3\) मिलता है। ऋण से भाग देने पर चिन्ह बदलता है।
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यदि \(x\in\mathbb{Z}\) और \(3x-4\geq8\) है तो सबसे छोटा हल कौन सा है?
If \(x\in\mathbb{Z}\) and \(3x-4\geq8\), what is the smallest solution?
#linear-inequalities
#integers
#least-value
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A (4)
B (3)
C (5)
D (12)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(3x\geq12\) and \(x\geq4\). Among integers the smallest value is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives \(3x\geq12\) and \(x\geq4\). Among integers the smallest value is (4).
Step 3
Exam Tip
असमानता से \(3x\geq12\) और \(x\geq4\) मिलता है। पूर्णांकों में सबसे छोटा मान (4) है।
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यदि \(x\in\mathbb{Z}\) और (5-2x> -7) है तो सबसे बड़ा हल कौन सा है?
If \(x\in\mathbb{Z}\) and (5-2x> -7), what is the greatest solution?
#linear-inequalities
#integers
#greatest-value
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A (5)
B (6)
C (4)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (5-2x>-7) we get (-2x>-12) and (x<6). The greatest integer solution is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). From (5-2x>-7) we get (-2x>-12) and (x<6). The greatest integer solution is (5).
Step 3
Exam Tip
(5-2x>-7) से (-2x>-12) और (x<6) मिलता है। पूर्णांकों में सबसे बड़ा मान (5) है।
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कौन सा मान असमानता (4x-9<3) को संतुष्ट करता है?
Which value satisfies the inequality (4x-9<3)?
#linear-inequalities
#value-checking
#exam-oriented
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A (x=2)
B (x=3)
C (x=4)
D (x=5)
Explanation opens after your attempt
Step 1
Concept
The solution is (x<3) so (x=2) satisfies it. Finding the general solution first is faster than testing all options.
Step 2
Why this answer is correct
The correct answer is A. (x=2). The solution is (x<3) so (x=2) satisfies it. Finding the general solution first is faster than testing all options.
Step 3
Exam Tip
हल (x<3) है इसलिए (x=2) संतुष्ट करता है। विकल्प जांचते समय पहले सामान्य हल निकालना तेज रहता है।
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कौन सा मान असमानता \(7-3x\leq1\) का हल नहीं है?
Which value is not a solution of \(7-3x\leq1\)?
#linear-inequalities
#value-checking
#not-solution
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A (x=1)
B (x=2)
C (x=3)
D (x=4)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(-3x\leq-6\) and \(x\geq2\). Hence (x=1) is not a solution.
Step 2
Why this answer is correct
The correct answer is A. (x=1). The inequality gives \(-3x\leq-6\) and \(x\geq2\). Hence (x=1) is not a solution.
Step 3
Exam Tip
असमानता से \(-3x\leq-6\) और \(x\geq2\) मिलता है। इसलिए (x=1) हल नहीं है।
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असमानता (ax+b>c) में यदि (a<0) हो तो (a) से भाग देते समय क्या होगा?
In (ax+b>c), if (a<0), what happens when dividing by (a)?
#linear-inequalities
#conceptual
#negative-division
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A असमानता का चिन्ह पलटेगा / The inequality sign reverses
B असमानता का चिन्ह वही रहेगा / The inequality sign remains same
C हल हमेशा रिक्त होगा / The solution is always empty
D हल हमेशा सभी वास्तविक संख्याएं होगा / The solution is all real numbers
Explanation opens after your attempt
Correct Answer
A. असमानता का चिन्ह पलटेगा / The inequality sign reverses
Step 1
Concept
Dividing by a negative number reverses the order of an inequality. This is the most common mistake in linear inequalities.
Step 2
Why this answer is correct
The correct answer is A. असमानता का चिन्ह पलटेगा / The inequality sign reverses. Dividing by a negative number reverses the order of an inequality. This is the most common mistake in linear inequalities.
Step 3
Exam Tip
ऋण संख्या से भाग देने पर असमानता का क्रम उलट जाता है। यह रैखिक असमानताओं की सबसे सामान्य गलती है।
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कौन सा चरण असमानता (-5x<20) के लिए सही है?
Which step is correct for the inequality (-5x<20)?
#linear-inequalities
#common-mistake
#negative-division
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A (x>-4)
B (x<-4)
C (x>4)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
Dividing by (-5) reverses the sign so (x>-4). Always apply the negative division rule.
Step 2
Why this answer is correct
The correct answer is A. (x>-4). Dividing by (-5) reverses the sign so (x>-4). Always apply the negative division rule.
Step 3
Exam Tip
(-5) से भाग देने पर चिन्ह पलटता है इसलिए (x>-4) मिलता है। ऋण भाग का नियम हमेशा लागू करें।
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विद्यार्थी ने \( -2x\geq10\) से \(x\geq-5\) लिखा। सही हल क्या है?
A student wrote \(x\geq-5\) from \(-2x\geq10\). What is the correct solution?
#linear-inequalities
#error-detection
#negative-coefficient
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A \(x\leq-5\)
B \(x\geq-5\)
C (x<-5)
D (x>-5)
Explanation opens after your attempt
Correct Answer
A. \(x\leq-5\)
Step 1
Concept
Dividing by (-2) reverses the sign to \(x\leq-5\). The mistake was not reversing the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq-5\). Dividing by (-2) reverses the sign to \(x\leq-5\). The mistake was not reversing the sign.
Step 3
Exam Tip
(-2) से भाग देने पर चिन्ह बदलकर \(x\leq-5\) होता है। गलती यह थी कि चिन्ह नहीं पलटा गया।
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किस असमानता का हल (x<4) है?
Which inequality has solution (x<4)?
#linear-inequalities
#reverse-question
#solution-matching
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A (3x+2<14)
B (3x+2>14)
C (3x-2>10)
D \(2x+3\geq11\)
Explanation opens after your attempt
Correct Answer
A. (3x+2<14)
Step 1
Concept
The inequality (3x+2<14) gives (3x<12) and (x<4). Solve each option before matching.
Step 2
Why this answer is correct
The correct answer is A. (3x+2<14). The inequality (3x+2<14) gives (3x<12) and (x<4). Solve each option before matching.
Step 3
Exam Tip
(3x+2<14) से (3x<12) और (x<4) मिलता है। विकल्पों को हल करके ही मिलान करें।
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किस असमानता का हल \(x\geq-2\) है?
Which inequality has solution \(x\geq-2\)?
#linear-inequalities
#reverse-question
#closed-inequality
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A \(4x+8\geq0\)
B \(4x+8\leq0\)
C (x+2<0)
D \(2x-4\geq0\)
Explanation opens after your attempt
Correct Answer
A. \(4x+8\geq0\)
Step 1
Concept
The inequality \(4x+8\geq0\) gives \(4x\geq-8\) and \(x\geq-2\). Identifying the boundary value is useful.
Step 2
Why this answer is correct
The correct answer is A. \(4x+8\geq0\). The inequality \(4x+8\geq0\) gives \(4x\geq-8\) and \(x\geq-2\). Identifying the boundary value is useful.
Step 3
Exam Tip
\(4x+8\geq0\) से \(4x\geq-8\) और \(x\geq-2\) मिलता है। सीमा मान पहचानना उपयोगी है।
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संख्या रेखा पर खुला बिंदु (3) पर है और रेखा बाईं ओर छायांकित है। असमानता क्या है?
On a number line there is an open point at (3) and shading to the left. What is the inequality?
#linear-inequalities
#number-line
#interval
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A (x<3)
B \(x\leq3\)
C (x>3)
D \(x\geq3\)
Explanation opens after your attempt
Step 1
Concept
An open point excludes equality and left shading shows smaller values. Therefore the inequality is (x<3).
Step 2
Why this answer is correct
The correct answer is A. (x<3). An open point excludes equality and left shading shows smaller values. Therefore the inequality is (x<3).
Step 3
Exam Tip
खुला बिंदु बराबरी को हटाता है और बाईं ओर छोटे मान दिखाता है। इसलिए असमानता (x<3) है।
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संख्या रेखा पर बंद बिंदु (-2) पर है और रेखा दाईं ओर छायांकित है। असमानता चुनिए।
On a number line there is a closed point at (-2) and shading to the right. Choose the inequality.
#linear-inequalities
#number-line
#closed-endpoint
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A \(x\geq-2\)
B (x>-2)
C \(x\leq-2\)
D (x<-2)
Explanation opens after your attempt
Correct Answer
A. \(x\geq-2\)
Step 1
Concept
A closed point includes equality and right shading represents larger values. Hence \(x\geq-2\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq-2\). A closed point includes equality and right shading represents larger values. Hence \(x\geq-2\) is correct.
Step 3
Exam Tip
बंद बिंदु बराबरी को शामिल करता है और दाईं ओर बड़े मान होते हैं। इसलिए \(x\geq-2\) सही है।
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असमानता (x+4>9) का संख्या रेखा पर सही वर्णन क्या है?
What is the correct number line description for (x+4>9)?
#linear-inequalities
#number-line
#solution-representation
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A (5) पर खुला बिंदु और दाईं ओर छाया / Open point at (5) and shading right
B (5) पर बंद बिंदु और दाईं ओर छाया / Closed point at (5) and shading right
C (5) पर खुला बिंदु और बाईं ओर छाया / Open point at (5) and shading left
D (5) पर बंद बिंदु और बाईं ओर छाया / Closed point at (5) and shading left
Explanation opens after your attempt
Correct Answer
A. (5) पर खुला बिंदु और दाईं ओर छाया / Open point at (5) and shading right
Step 1
Concept
The solution is (x>5). A strict greater sign gives an open point and right direction.
Step 2
Why this answer is correct
The correct answer is A. (5) पर खुला बिंदु और दाईं ओर छाया / Open point at (5) and shading right. The solution is (x>5). A strict greater sign gives an open point and right direction.
Step 3
Exam Tip
हल (x>5) है। कठोर बड़ा चिन्ह खुला बिंदु और दाईं दिशा देता है।
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एक संख्या में (6) जोड़ने पर परिणाम (20) से कम है। संख्या (x) के लिए असमानता का हल क्या है?
When (6) is added to a number, the result is less than (20). What is the solution for the number (x)?
#linear-inequalities
#word-problem
#translation
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A (x<14)
B (x>14)
C \(x\leq14\)
D \(x\geq14\)
Explanation opens after your attempt
Step 1
Concept
The situation gives (x+6<20) and hence (x<14). In word problems form the inequality first.
Step 2
Why this answer is correct
The correct answer is A. (x<14). The situation gives (x+6<20) and hence (x<14). In word problems form the inequality first.
Step 3
Exam Tip
स्थिति (x+6<20) देती है और इससे (x<14) मिलता है। शब्द प्रश्न में पहले असमानता बनाएं।
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किसी संख्या का (4) गुना (28) से अधिक नहीं है। संख्या (x) के लिए हल क्या है?
Four times a number is not more than (28). What is the solution for (x)?
#linear-inequalities
#word-problem
#not-more-than
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A \(x\leq7\)
B (x<7)
C \(x\geq7\)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(x\leq7\)
Step 1
Concept
The statement gives \(4x\leq28\) so \(x\leq7\). The phrase not more than means \(\leq\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq7\). The statement gives \(4x\leq28\) so \(x\leq7\). The phrase not more than means \(\leq\).
Step 3
Exam Tip
वाक्य \(4x\leq28\) देता है इसलिए \(x\leq7\) है। वाक्यांश not more than का अर्थ \(\leq\) होता है।
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एक परीक्षा में उत्तीर्ण होने के लिए कम से कम (33) अंक चाहिए। यदि रवि के अंक (m) हैं तो सही असमानता कौन सी है?
At least (33) marks are needed to pass an exam. If Ravi has marks (m), which inequality is correct?
#linear-inequalities
#word-problem
#at-least
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A \(m\geq33\)
B (m>33)
C \(m\leq33\)
D (m<33)
Explanation opens after your attempt
Correct Answer
A. \(m\geq33\)
Step 1
Concept
At least includes the boundary value so \(m\geq33\). Pay attention to equality in such phrases.
Step 2
Why this answer is correct
The correct answer is A. \(m\geq33\). At least includes the boundary value so \(m\geq33\). Pay attention to equality in such phrases.
Step 3
Exam Tip
कम से कम में सीमा मान शामिल होता है इसलिए \(m\geq33\) है। ऐसे शब्दों में बराबरी पर ध्यान दें।
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किसी क्लब में प्रवेश के लिए आयु (18) वर्ष से अधिक होनी चाहिए। आयु (a) के लिए सही असमानता क्या है?
To enter a club, age must be more than (18) years. What is the correct inequality for age (a)?
#linear-inequalities
#word-problem
#more-than
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A (a>18)
B \(a\geq18\)
C (a<18)
D \(a\leq18\)
Explanation opens after your attempt
Step 1
Concept
More than means strictly greater so (a>18). If the age is exactly (18), the condition is not satisfied.
Step 2
Why this answer is correct
The correct answer is A. (a>18). More than means strictly greater so (a>18). If the age is exactly (18), the condition is not satisfied.
Step 3
Exam Tip
more than का अर्थ कठोर रूप से बड़ा है इसलिए (a>18) है। यदि exactly (18) हो तो यह शर्त पूरी नहीं होती।
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असमानता \(3x+2\leq11\) में (x) का सबसे बड़ा पूर्णांक मान क्या है?
What is the greatest integer value of (x) in \(3x+2\leq11\)?
#linear-inequalities
#integer-value
#greatest
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A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The inequality \(3x+2\leq11\) gives \(x\leq3\). Hence the greatest integer value is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The inequality \(3x+2\leq11\) gives \(x\leq3\). Hence the greatest integer value is (3).
Step 3
Exam Tip
\(3x+2\leq11\) से \(x\leq3\) मिलता है। इसलिए सबसे बड़ा पूर्णांक मान (3) है।
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असमानता (5x-1>14) में (x) का सबसे छोटा प्राकृतिक मान क्या है?
What is the least natural value of (x) in (5x-1>14)?
#linear-inequalities
#natural-numbers
#least-value
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A (4)
B (3)
C (5)
D (2)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (5x>15) and (x>3). The least natural value is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives (5x>15) and (x>3). The least natural value is (4).
Step 3
Exam Tip
असमानता से (5x>15) और (x>3) मिलता है। प्राकृतिक संख्याओं में सबसे छोटा मान (4) है।
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असमानता \(-1\leq x<4\) और \(x\in\mathbb{Z}\) के लिए कितने हल हैं?
How many solutions are there for \(-1\leq x<4\) and \(x\in\mathbb{Z}\)?
#linear-inequalities
#integers
#counting-solutions
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A (5)
B (4)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The integer solutions are ({-1,0,1,2,3}). Hence there are (5) solutions.
Step 2
Why this answer is correct
The correct answer is A. (5). The integer solutions are ({-1,0,1,2,3}). Hence there are (5) solutions.
Step 3
Exam Tip
पूर्णांक हल ({-1,0,1,2,3}) हैं। इसलिए कुल (5) हल मिलते हैं।
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यदि (x=2) असमानता \(kx+1\leq9\) को संतुष्ट करे और (k>0) हो तो (k) पर शर्त क्या है?
If (x=2) satisfies \(kx+1\leq9\) and (k>0), what is the condition on (k)?
#linear-inequalities
#parameter
#substitution
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A \(0<k\leq4\)
B (k>4)
C \(k\leq0\)
D \(k\geq5\)
Explanation opens after your attempt
Correct Answer
A. \(0<k\leq4\)
Step 1
Concept
Putting (x=2) gives \(2k+1\leq9\), so \(k\leq4\). Also include the given condition (k>0).
Step 2
Why this answer is correct
The correct answer is A. \(0<k\leq4\). Putting (x=2) gives \(2k+1\leq9\), so \(k\leq4\). Also include the given condition (k>0).
Step 3
Exam Tip
(x=2) रखने पर \(2k+1\leq9\) से \(k\leq4\) मिलता है। साथ में दी गई शर्त (k>0) भी जोड़ें।
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यदि असमानता (x+2<k) का हल (x<7) है तो (k) का मान क्या है?
If the inequality (x+2<k) has solution (x<7), what is the value of (k)?
#linear-inequalities
#parameter
#solution-boundary
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A (9)
B (5)
C (7)
D (2)
Explanation opens after your attempt
Step 1
Concept
From (x+2<k), we get (x<k-2). Setting (k-2=7) gives (k=9).
Step 2
Why this answer is correct
The correct answer is A. (9). From (x+2<k), we get (x<k-2). Setting (k-2=7) gives (k=9).
Step 3
Exam Tip
(x+2<k) से (x<k-2) मिलता है। (k-2=7) रखने पर (k=9) है।
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कौन सी असमानता सभी वास्तविक (x) के लिए सत्य है?
Which inequality is true for all real (x)?
#linear-inequalities
#all-real-solutions
#conceptual
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A (2x+3<2x+5)
B (2x+5<2x+3)
C (x+1<x-1)
D (3x>3x+1)
Explanation opens after your attempt
Correct Answer
A. (2x+3<2x+5)
Step 1
Concept
Subtracting (2x) gives (3<5), which is always true. When the variable cancels, check the truth of the remaining statement.
Step 2
Why this answer is correct
The correct answer is A. (2x+3<2x+5). Subtracting (2x) gives (3<5), which is always true. When the variable cancels, check the truth of the remaining statement.
Step 3
Exam Tip
(2x) घटाने पर (3<5) मिलता है जो हमेशा सत्य है। चर मिटने पर बची हुई कथन की सत्यता जांचें।
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असमानता \(2(x+3)-x\geq10\) का हल क्या है?
What is the solution of \(2(x+3)-x\geq10\)?
#linear-inequalities
#simplification
#brackets
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A \(x\geq4\)
B \(x\leq4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\geq4\)
Step 1
Concept
Simplifying gives \(x+6\geq10\) and hence \(x\geq4\). Combine like terms first and then solve.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq4\). Simplifying gives \(x+6\geq10\) and hence \(x\geq4\). Combine like terms first and then solve.
Step 3
Exam Tip
सरल करने पर \(x+6\geq10\) और इसलिए \(x\geq4\) मिलता है। पहले समान पद जोड़ें फिर हल करें।
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असमानता \(\frac{x+4}{2}-\frac{x-2}{3}<5\) का हल चुनिए।
Choose the solution of \(\frac{x+4}{2}-\frac{x-2}{3}<5\).
#linear-inequalities
#fractions
#lcm-method
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A (x<20)
B (x>20)
C (x<10)
D (x>10)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (6) gives (3(x+4)-2(x-2)<30). Simplifying gives (x+16<30), so the correct result is (x<14).
Step 2
Why this answer is correct
The correct answer is A. (x<20). Multiplying by (6) gives (3(x+4)-2(x-2)<30). Simplifying gives (x+16<30), so the correct result is (x<14).
Step 3
Exam Tip
(6) से गुणा करने पर (3(x+4)-2(x-2)<30) मिलता है। सरल करने पर (x+16<30) से (x<14) नहीं बल्कि (x<14) आता है।
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असमानता \(\frac{2x-5}{4}+1\geq3\) का हल क्या है?
What is the solution of the inequality \(\frac{2x-5}{4}+1\geq3\)?
#linear-inequalities
#fraction
#algebraic-solution
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A \(x\geq\frac{13}{2}\)
B \(x\leq\frac{13}{2}\)
C \(x\geq\frac{7}{2}\)
D \(x\leq\frac{7}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x\geq\frac{13}{2}\)
Step 1
Concept
Subtracting (1) gives \(\frac{2x-5}{4}\geq2\) and then \(2x-5\geq8\). Hence \(x\geq\frac{13}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq\frac{13}{2}\). Subtracting (1) gives \(\frac{2x-5}{4}\geq2\) and then \(2x-5\geq8\). Hence \(x\geq\frac{13}{2}\).
Step 3
Exam Tip
(1) घटाने पर \(\frac{2x-5}{4}\geq2\) और फिर \(2x-5\geq8\) मिलता है। इसलिए \(x\geq\frac{13}{2}\) है।
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असमानता \(3-\frac{x+2}{5}<1\) को हल कीजिए।
Solve the inequality \(3-\frac{x+2}{5}<1\).
#linear-inequalities
#negative-term
#fraction
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A (x>8)
B (x<8)
C (x>-8)
D (x<-8)
Explanation opens after your attempt
Step 1
Concept
Subtracting (3) gives \(-\frac{x+2}{5}< -2\). Removing the negative term reverses the sign and gives (x>8).
Step 2
Why this answer is correct
The correct answer is A. (x>8). Subtracting (3) gives \(-\frac{x+2}{5}< -2\). Removing the negative term reverses the sign and gives (x>8).
Step 3
Exam Tip
(3) घटाने पर \(-\frac{x+2}{5}< -2\) मिलता है। ऋण पद हटाने पर चिन्ह बदलता है और (x>8) मिलता है।
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युग्म असमानता \(-3\leq\frac{x+1}{2}<4\) का हल चुनिए।
Choose the solution of the compound inequality \(-3\leq\frac{x+1}{2}<4\).
#linear-inequalities
#compound-inequality
#interval
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A \(-7\leq x<7\)
B \(-7<x\leq7\)
C \(x\leq-7\)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(-7\leq x<7\)
Step 1
Concept
Multiplying by (2) gives \(-6\leq x+1<8\). Subtracting (1) gives the correct solution \(-7\leq x<7\).
Step 2
Why this answer is correct
The correct answer is A. \(-7\leq x<7\). Multiplying by (2) gives \(-6\leq x+1<8\). Subtracting (1) gives the correct solution \(-7\leq x<7\).
Step 3
Exam Tip
(2) से गुणा करने पर \(-6\leq x+1<8\) मिलता है। (1) घटाने पर \(-7\leq x<7\) सही हल है।
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यदि \(x\in\mathbb{Z}\) और \(\frac{x-3}{2}>1\) है तो सबसे छोटा पूर्णांक हल कौन सा है?
If \(x\in\mathbb{Z}\) and \(\frac{x-3}{2}>1\), what is the least integer solution?
#linear-inequalities
#integers
#least-value
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A (6)
B (5)
C (4)
D (3)
Explanation opens after your attempt
Step 1
Concept
The inequality \(\frac{x-3}{2}>1\) gives (x-3>2) and (x>5). Therefore the least integer solution is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The inequality \(\frac{x-3}{2}>1\) gives (x-3>2) and (x>5). Therefore the least integer solution is (6).
Step 3
Exam Tip
\(\frac{x-3}{2}>1\) से (x-3>2) और (x>5) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (6) है।
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किसी संख्या के दोगुने में से (5) घटाने पर परिणाम कम से कम (13) है। संख्या (x) के लिए हल क्या है?
When (5) is subtracted from twice a number, the result is at least (13). What is the solution for (x)?
#linear-inequalities
#word-problem
#at-least
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A \(x\geq9\)
B (x>9)
C \(x\leq9\)
D (x<9)
Explanation opens after your attempt
Correct Answer
A. \(x\geq9\)
Step 1
Concept
The situation gives \(2x-5\geq13\). This gives \(2x\geq18\) and \(x\geq9\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq9\). The situation gives \(2x-5\geq13\). This gives \(2x\geq18\) and \(x\geq9\).
Step 3
Exam Tip
स्थिति \(2x-5\geq13\) देती है। इससे \(2x\geq18\) और \(x\geq9\) मिलता है।
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असमानता (5(x-1)+2<5x) का हल समुच्चय क्या है?
What is the solution set of the inequality (5(x-1)+2<5x)?
#linear-inequalities
#all-real-solutions
#simplification
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A सभी \(x\in\mathbb{R}\) / All \(x\in\mathbb{R}\)
B कोई वास्तविक हल नहीं / No real solution
C केवल (x=0) / Only (x=0)
D केवल (x>0) / Only (x>0)
Explanation opens after your attempt
Correct Answer
A. सभी \(x\in\mathbb{R}\) / All \(x\in\mathbb{R}\)
Step 1
Concept
Simplifying gives (5x-3<5x). Subtracting (5x) gives (-3<0), which is true, so all real (x) are solutions.
Step 2
Why this answer is correct
The correct answer is A. सभी \(x\in\mathbb{R}\) / All \(x\in\mathbb{R}\). Simplifying gives (5x-3<5x). Subtracting (5x) gives (-3<0), which is true, so all real (x) are solutions.
Step 3
Exam Tip
सरल करने पर (5x-3<5x) मिलता है। (5x) घटाने पर (-3<0) सत्य है इसलिए सभी वास्तविक (x) हल हैं।
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असमानता \(\frac{3x-1}{2}\leq x+4\) का हल क्या है?
What is the solution of the inequality \(\frac{3x-1}{2}\leq x+4\)?
#linear-inequalities
#variables-both-sides
#fraction
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A \(x\leq9\)
B \(x\geq9\)
C \(x\leq7\)
D \(x\geq7\)
Explanation opens after your attempt
Correct Answer
A. \(x\leq9\)
Step 1
Concept
Multiplying by (2) gives \(3x-1\leq2x+8\). Combining like terms gives the correct solution \(x\leq9\).
Step 2
Why this answer is correct
The correct answer is A. \(x\leq9\). Multiplying by (2) gives \(3x-1\leq2x+8\). Combining like terms gives the correct solution \(x\leq9\).
Step 3
Exam Tip
(2) से गुणा करने पर \(3x-1\leq2x+8\) मिलता है। समान पद मिलाने पर \(x\leq9\) सही हल है।
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