असमानता (x+5>12) का हल क्या है?
What is the solution of the inequality (x+5>12)?
#linear inequalities
#one variable
#addition
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A (x>7)
B (x<7)
C \(x\ge 7\)
D \(x\le 7\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (5) from both sides gives (x>7). In exams, apply the same operation on both sides.
Step 2
Why this answer is correct
The correct answer is A. (x>7). Subtracting (5) from both sides gives (x>7). In exams, apply the same operation on both sides.
Step 3
Exam Tip
दोनों पक्षों से (5) घटाने पर (x>7) मिलता है। परीक्षा में समान संख्या दोनों पक्षों पर लगाएं।
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असमानता \(x-4\le 9\) का हल क्या है?
What is the solution of the inequality \(x-4\le 9\)?
#linear inequalities
#one variable
#subtraction
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A \(x\le 13\)
B \(x\ge 13\)
C (x<13)
D (x>13)
Explanation opens after your attempt
Correct Answer
A. \(x\le 13\)
Step 1
Concept
Adding (4) to both sides gives \(x\le 13\). The sign does not change because addition is used.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 13\). Adding (4) to both sides gives \(x\le 13\). The sign does not change because addition is used.
Step 3
Exam Tip
दोनों पक्षों में (4) जोड़ने पर \(x\le 13\) मिलता है। चिह्न नहीं बदलता क्योंकि जोड़ किया गया है।
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असमानता \(5x+2\ge 17\) का हल क्या है?
What is the solution of the inequality \(5x+2\ge 17\)?
#linear inequalities
#two step
#easy
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A \(x\ge 3\)
B \(x\le 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
First subtract (2), then divide by (5), giving \(x\ge 3\). Keep the equality part of the sign till the end.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). First subtract (2), then divide by (5), giving \(x\ge 3\). Keep the equality part of the sign till the end.
Step 3
Exam Tip
पहले (2) घटाएं और फिर (5) से भाग दें, तब \(x\ge 3\)। बराबरी वाला चिह्न अंत तक बनाए रखें।
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असमानता (4x-7<9) का हल क्या है?
What is the solution of the inequality (4x-7<9)?
#linear inequalities
#two step
#constant term
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A (x<4)
B (x>4)
C \(x\le 4\)
D \(x\ge 4\)
Explanation opens after your attempt
Step 1
Concept
Adding (7) to both sides gives (4x<16), so (x<4). Removing the constant term first is easier.
Step 2
Why this answer is correct
The correct answer is A. (x<4). Adding (7) to both sides gives (4x<16), so (x<4). Removing the constant term first is easier.
Step 3
Exam Tip
दोनों पक्षों में (7) जोड़कर (4x<16), इसलिए (x<4)। पहले स्थिर पद हटाना आसान रहता है।
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असमानता \(7-2x\le 1\) का हल क्या है?
What is the solution of the inequality \(7-2x\le 1\)?
#linear inequalities
#negative coefficient
#sign reversal
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A \(x\ge 3\)
B \(x\le 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
Subtracting (7) gives \(-2x\le -6\), then division by (-2) reverses the sign to \(x\ge 3\). Be careful with a negative coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). Subtracting (7) gives \(-2x\le -6\), then division by (-2) reverses the sign to \(x\ge 3\). Be careful with a negative coefficient.
Step 3
Exam Tip
(7) घटाने पर \(-2x\le -6\), फिर (-2) से भाग देने पर चिह्न पलटकर \(x\ge 3\) होता है। ऋणात्मक गुणांक पर विशेष ध्यान दें।
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असमानता (2x+3<x+8) का हल क्या है?
What is the solution of the inequality (2x+3<x+8)?
#linear inequalities
#variables both sides
#easy
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A (x<5)
B (x>5)
C \(x\le 5\)
D \(x\ge 5\)
Explanation opens after your attempt
Step 1
Concept
Removing (x) and (3) from both sides gives (x<5). Keep variable terms on one side.
Step 2
Why this answer is correct
The correct answer is A. (x<5). Removing (x) and (3) from both sides gives (x<5). Keep variable terms on one side.
Step 3
Exam Tip
दोनों पक्षों से (x) और (3) हटाने पर (x<5) मिलता है। चर पदों को एक तरफ रखें।
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असमानता \(6x-1\ge 2x+11\) का हल क्या है?
What is the solution of the inequality \(6x-1\ge 2x+11\)?
#linear inequalities
#variables both sides
#simplification
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A \(x\ge 3\)
B \(x\le 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
Subtracting (2x) and adding (1) gives \(4x\ge 12\), so \(x\ge 3\). Combine like terms carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). Subtracting (2x) and adding (1) gives \(4x\ge 12\), so \(x\ge 3\). Combine like terms carefully.
Step 3
Exam Tip
(2x) घटाने और (1) जोड़ने पर \(4x\ge 12\), इसलिए \(x\ge 3\)। समान पदों को सावधानी से मिलाएं।
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असमानता (3(x+2)>15) का हल क्या है?
What is the solution of the inequality (3(x+2)>15)?
#linear inequalities
#brackets
#positive factor
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A (x>3)
B (x<3)
C \(x\ge 3\)
D \(x\le 3\)
Explanation opens after your attempt
Step 1
Concept
Dividing by (3) gives (x+2>5), so (x>3). You may open brackets or divide first.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Dividing by (3) gives (x+2>5), so (x>3). You may open brackets or divide first.
Step 3
Exam Tip
(3) से भाग देने पर (x+2>5), इसलिए (x>3)। कोष्ठक खोलना या पहले भाग देना दोनों ठीक हैं।
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असमानता \(2(x-5)\le 8\) का हल क्या है?
What is the solution of the inequality \(2(x-5)\le 8\)?
#linear inequalities
#brackets
#less than equal
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A \(x\le 9\)
B \(x\ge 9\)
C (x<9)
D (x>9)
Explanation opens after your attempt
Correct Answer
A. \(x\le 9\)
Step 1
Concept
Dividing by (2) gives \(x-5\le 4\), so \(x\le 9\). A positive multiplier keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 9\). Dividing by (2) gives \(x-5\le 4\), so \(x\le 9\). A positive multiplier keeps the sign unchanged.
Step 3
Exam Tip
(2) से भाग देने पर \(x-5\le 4\), इसलिए \(x\le 9\)। धनात्मक गुणक से चिह्न वही रहता है।
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असमानता \(\frac{x-1}{4}\ge 2\) का हल क्या है?
What is the solution of the inequality \(\frac{x-1}{4}\ge 2\)?
#linear inequalities
#fractions
#greater than equal
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A \(x\ge 9\)
B \(x\le 9\)
C (x>9)
D (x<9)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 9\)
Step 1
Concept
Multiplying both sides by (4) gives \(x-1\ge 8\), so \(x\ge 9\). A positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 9\). Multiplying both sides by (4) gives \(x-1\ge 8\), so \(x\ge 9\). A positive denominator does not change the sign.
Step 3
Exam Tip
दोनों पक्षों को (4) से गुणा करने पर \(x-1\ge 8\), इसलिए \(x\ge 9\)। धनात्मक हर चिह्न नहीं बदलता।
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असमानता \(\frac{2x+1}{5}\le 3\) का हल क्या है?
What is the solution of the inequality \(\frac{2x+1}{5}\le 3\)?
#linear inequalities
#fractions
#two step
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A \(x\le 7\)
B \(x\ge 7\)
C (x<7)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(x\le 7\)
Step 1
Concept
Multiplying by (5) gives \(2x+1\le 15\), so \(x\le 7\). Removing the fraction first is a good method.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 7\). Multiplying by (5) gives \(2x+1\le 15\), so \(x\le 7\). Removing the fraction first is a good method.
Step 3
Exam Tip
(5) से गुणा करने पर \(2x+1\le 15\), इसलिए \(x\le 7\)। पहले भिन्न हटाना अच्छा तरीका है।
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असमानता \(-\frac{x}{4}<2\) का हल क्या है?
What is the solution of the inequality \(-\frac{x}{4}<2\)?
#linear inequalities
#negative multiplier
#fractions
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A (x>-8)
B (x<-8)
C (x>8)
D (x<8)
Explanation opens after your attempt
Step 1
Concept
Multiplying both sides by (-4) reverses the sign and gives (x>-8). Reverse the sign when multiplying by a negative number.
Step 2
Why this answer is correct
The correct answer is A. (x>-8). Multiplying both sides by (-4) reverses the sign and gives (x>-8). Reverse the sign when multiplying by a negative number.
Step 3
Exam Tip
दोनों पक्षों को (-4) से गुणा करने पर चिह्न पलटता है और (x>-8) मिलता है। ऋणात्मक से गुणा करते समय चिह्न बदलें।
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असमानता (9-3x>0) का हल क्या है?
What is the solution of the inequality (9-3x>0)?
#linear inequalities
#zero comparison
#sign reversal
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A (x<3)
B (x>3)
C \(x\le 3\)
D \(x\ge 3\)
Explanation opens after your attempt
Step 1
Concept
From (9-3x>0), we get (-3x>-9), so division by (-3) gives (x<3). Reversing the sign is necessary in negative division.
Step 2
Why this answer is correct
The correct answer is A. (x<3). From (9-3x>0), we get (-3x>-9), so division by (-3) gives (x<3). Reversing the sign is necessary in negative division.
Step 3
Exam Tip
(9-3x>0) से (-3x>-9), इसलिए (-3) से भाग देने पर (x<3)। ऋणात्मक भाग में चिह्न पलटना जरूरी है।
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असमानता \(2x+5\le x+12\) का हल क्या है?
What is the solution of the inequality \(2x+5\le x+12\)?
#linear inequalities
#variables both sides
#easy
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A \(x\le 7\)
B \(x\ge 7\)
C (x<7)
D (x>7)
Explanation opens after your attempt
Correct Answer
A. \(x\le 7\)
Step 1
Concept
Subtracting (x) from both sides gives \(x+5\le 12\), so \(x\le 7\). Isolating the variable is the key step.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 7\). Subtracting (x) from both sides gives \(x+5\le 12\), so \(x\le 7\). Isolating the variable is the key step.
Step 3
Exam Tip
दोनों पक्षों से (x) घटाने पर \(x+5\le 12\), इसलिए \(x\le 7\)। चर को अकेला करना मुख्य कदम है।
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असमानता (10-x<4) का हल क्या है?
What is the solution of the inequality (10-x<4)?
#linear inequalities
#negative variable
#common mistake
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A (x>6)
B (x<6)
C \(x\ge 6\)
D \(x\le 6\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (10) gives (-x<-6), then dividing by (-1) gives (x>6). The sign reverses when changing (-x) to (x).
Step 2
Why this answer is correct
The correct answer is A. (x>6). Subtracting (10) gives (-x<-6), then dividing by (-1) gives (x>6). The sign reverses when changing (-x) to (x).
Step 3
Exam Tip
(10) घटाने पर (-x<-6), फिर (-1) से भाग देने पर (x>6)। (-x) को (x) बनाते समय चिह्न पलटता है।
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असमानता \(4(x+1)\ge 2(x+5)\) का हल क्या है?
What is the solution of the inequality \(4(x+1)\ge 2(x+5)\)?
#linear inequalities
#brackets
#variables both sides
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A \(x\ge 3\)
B \(x\le 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 3\)
Step 1
Concept
Opening brackets gives \(4x+4\ge 2x+10\), so \(2x\ge 6\) and \(x\ge 3\). Open brackets correctly first.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 3\). Opening brackets gives \(4x+4\ge 2x+10\), so \(2x\ge 6\) and \(x\ge 3\). Open brackets correctly first.
Step 3
Exam Tip
कोष्ठक खोलने पर \(4x+4\ge 2x+10\), इसलिए \(2x\ge 6\) और \(x\ge 3\)। पहले कोष्ठक सही खोलें।
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असमानता (5(x-2)<3x+4) का हल क्या है?
What is the solution of the inequality (5(x-2)<3x+4)?
#linear inequalities
#brackets
#transposition
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A (x<7)
B (x>7)
C \(x\le 7\)
D \(x\ge 7\)
Explanation opens after your attempt
Step 1
Concept
From (5x-10<3x+4), we get (2x<14), so (x<7). Keep variable terms on one side and numbers on the other.
Step 2
Why this answer is correct
The correct answer is A. (x<7). From (5x-10<3x+4), we get (2x<14), so (x<7). Keep variable terms on one side and numbers on the other.
Step 3
Exam Tip
(5x-10<3x+4) से (2x<14), इसलिए (x<7)। चर पदों को एक तरफ और संख्याओं को दूसरी तरफ रखें।
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यदि (x) एक पूर्णांक है और (x+2<6), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (x+2<6), what is the greatest possible (x)?
#linear inequalities
#integer solution
#greatest integer
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x<4), so the greatest integer is (3). A strict sign does not include the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (3). The inequality gives (x<4), so the greatest integer is (3). A strict sign does not include the boundary value.
Step 3
Exam Tip
असमानता से (x<4) मिलता है, इसलिए सबसे बड़ा पूर्णांक (3) है। सख्त चिह्न पर सीमा मान शामिल नहीं होता।
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यदि (x) एक पूर्णांक है और \(2x\ge 10\), तो सबसे छोटा संभव (x) क्या है?
If (x) is an integer and \(2x\ge 10\), what is the least possible (x)?
#linear inequalities
#integer solution
#least integer
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A (5)
B (4)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
Dividing by (2) gives \(x\ge 5\), so the least integer is (5). The equality sign includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (5). Dividing by (2) gives \(x\ge 5\), so the least integer is (5). The equality sign includes the boundary value.
Step 3
Exam Tip
(2) से भाग देने पर \(x\ge 5\), इसलिए सबसे छोटा पूर्णांक (5) है। बराबरी वाला चिह्न सीमा मान को शामिल करता है।
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असमानता (3x+1>10) का अंतराल रूप कौन सा है?
Which interval form represents the solution of (3x+1>10)?
#linear inequalities
#interval notation
#open interval
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A \((3,\infty)\)
B \([3,\infty)\)
C \((-\infty,3)\)
D \((-\infty,3]\)
Explanation opens after your attempt
Correct Answer
A. \((3,\infty)\)
Step 1
Concept
The solution is (x>3), so the interval is (\(3,\infty\)). Use an open bracket for a strict inequality.
Step 2
Why this answer is correct
The correct answer is A. \((3,\infty)\). The solution is (x>3), so the interval is (\(3,\infty\)). Use an open bracket for a strict inequality.
Step 3
Exam Tip
हल (x>3) है, इसलिए अंतराल (\(3,\infty\)) होगा। सख्त असमानता में खुला कोष्ठक लगाएं।
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असमानता \(4x-8\le 0\) का अंतराल रूप कौन सा है?
Which interval form represents the solution of \(4x-8\le 0\)?
#linear inequalities
#interval notation
#closed endpoint
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A \((-\infty,2]\)
B \((-\infty,2)\)
C \([2,\infty)\)
D \((2,\infty)\)
Explanation opens after your attempt
Correct Answer
A. \((-\infty,2]\)
Step 1
Concept
From \(4x\le 8\), we get \(x\le 2\), so (\(-\infty,2]\). The sign \(\le\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. \((-\infty,2]\). From \(4x\le 8\), we get \(x\le 2\), so (\(-\infty,2]\). The sign \(\le\) includes the boundary value.
Step 3
Exam Tip
\(4x\le 8\) से \(x\le 2\) मिलता है, इसलिए (\(-\infty,2]\)। \(\le\) में सीमा मान शामिल होता है।
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कौन सा मान असमानता \(5-x\ge 2\) को संतुष्ट नहीं करता?
Which value does not satisfy the inequality \(5-x\ge 2\)?
#linear inequalities
#not satisfying
#negative variable
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A (x=4)
B (x=3)
C (x=2)
D (x=1)
Explanation opens after your attempt
Step 1
Concept
The solution is \(x\le 3\), so (x=4) does not satisfy it. Do not forget to reverse the sign with a negative (x).
Step 2
Why this answer is correct
The correct answer is A. (x=4). The solution is \(x\le 3\), so (x=4) does not satisfy it. Do not forget to reverse the sign with a negative (x).
Step 3
Exam Tip
हल \(x\le 3\) है, इसलिए (x=4) संतुष्ट नहीं करता। नकारात्मक (x) होने पर चिह्न पलटना न भूलें।
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असमानता \(x+9\ge 15\) हल करते समय पहला सही कदम कौन सा है?
What is the correct first step while solving \(x+9\ge 15\)?
#linear inequalities
#first step
#operation
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A दोनों पक्षों से (9) घटाएं / Subtract (9) from both sides
B दोनों पक्षों में (9) जोड़ें / Add (9) to both sides
C दोनों पक्षों को (9) से गुणा करें / Multiply both sides by (9)
D दोनों पक्षों को (-9) से भाग दें / Divide both sides by (-9)
Explanation opens after your attempt
Correct Answer
A. दोनों पक्षों से (9) घटाएं / Subtract (9) from both sides
Step 1
Concept
To isolate (x), subtract (9) from both sides. Choosing the inverse operation saves time in exams.
Step 2
Why this answer is correct
The correct answer is A. दोनों पक्षों से (9) घटाएं / Subtract (9) from both sides. To isolate (x), subtract (9) from both sides. Choosing the inverse operation saves time in exams.
Step 3
Exam Tip
(x) को अलग करने के लिए दोनों पक्षों से (9) घटाते हैं। उल्टा ऑपरेशन चुनना परीक्षा में समय बचाता है।
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असमानता \(-5x\le 20\) हल करते समय कौन सा नियम लागू होगा?
Which rule applies while solving \(-5x\le 20\)?
#linear inequalities
#rule
#negative division
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A (-5) से भाग देने पर चिह्न पलटेगा / Dividing by (-5) reverses the sign
B (-5) से भाग देने पर चिह्न वही रहेगा / Dividing by (-5) keeps the sign same
C (20) घटाने पर चिह्न पलटेगा / Subtracting (20) reverses the sign
D (5) जोड़ने पर चिह्न पलटेगा / Adding (5) reverses the sign
Explanation opens after your attempt
Correct Answer
A. (-5) से भाग देने पर चिह्न पलटेगा / Dividing by (-5) reverses the sign
Step 1
Concept
Dividing by a negative number reverses the inequality sign. This is the key rule in \(-5x\le 20\).
Step 2
Why this answer is correct
The correct answer is A. (-5) से भाग देने पर चिह्न पलटेगा / Dividing by (-5) reverses the sign. Dividing by a negative number reverses the inequality sign. This is the key rule in \(-5x\le 20\).
Step 3
Exam Tip
ऋणात्मक संख्या से भाग देने पर असमानता का चिह्न पलटता है। यही नियम \(-5x\le 20\) में मुख्य है।
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असमानता \(12\le 3x\) का हल क्या है?
What is the solution of the inequality \(12\le 3x\)?
#linear inequalities
#rewrite solution
#positive division
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A \(x\ge 4\)
B \(x\le 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
Dividing both sides by (3) gives \(4\le x\), that is \(x\ge 4\). Write the final answer starting with (x) in standard form.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). Dividing both sides by (3) gives \(4\le x\), that is \(x\ge 4\). Write the final answer starting with (x) in standard form.
Step 3
Exam Tip
दोनों पक्षों को (3) से भाग देने पर \(4\le x\), अर्थात \(x\ge 4\)। उत्तर को सामान्य रूप में (x) से शुरू करके लिखें।
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असमानता (18>6x) का हल क्या है?
What is the solution of the inequality (18>6x)?
#linear inequalities
#rewrite inequality
#less than
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A (x<3)
B (x>3)
C \(x\le 3\)
D \(x\ge 3\)
Explanation opens after your attempt
Step 1
Concept
Dividing by (6) gives (3>x), that is (x<3). Keep the direction correct when rewriting the inequality.
Step 2
Why this answer is correct
The correct answer is A. (x<3). Dividing by (6) gives (3>x), that is (x<3). Keep the direction correct when rewriting the inequality.
Step 3
Exam Tip
(6) से भाग देने पर (3>x), अर्थात (x<3)। असमानता को पलटकर लिखते समय दिशा सही रखें।
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असमानता \(2x+7\le 3\) का हल क्या है?
What is the solution of the inequality \(2x+7\le 3\)?
#linear inequalities
#negative answer
#two step
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A \(x\le -2\)
B \(x\ge -2\)
C (x<-2)
D (x>-2)
Explanation opens after your attempt
Correct Answer
A. \(x\le -2\)
Step 1
Concept
Subtracting (7) gives \(2x\le -4\), so \(x\le -2\). Dividing by positive (2) does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le -2\). Subtracting (7) gives \(2x\le -4\), so \(x\le -2\). Dividing by positive (2) does not change the sign.
Step 3
Exam Tip
(7) घटाने पर \(2x\le -4\), इसलिए \(x\le -2\)। धनात्मक (2) से भाग देने पर चिह्न नहीं बदलता।
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असमानता \(4-3x\ge 13\) का हल क्या है?
What is the solution of the inequality \(4-3x\ge 13\)?
#linear inequalities
#negative solution
#sign reversal
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A \(x\le -3\)
B \(x\ge -3\)
C (x<-3)
D (x>-3)
Explanation opens after your attempt
Correct Answer
A. \(x\le -3\)
Step 1
Concept
Subtracting (4) gives \(-3x\ge 9\), then division by (-3) gives \(x\le -3\). The sign reverses after negative division.
Step 2
Why this answer is correct
The correct answer is A. \(x\le -3\). Subtracting (4) gives \(-3x\ge 9\), then division by (-3) gives \(x\le -3\). The sign reverses after negative division.
Step 3
Exam Tip
(4) घटाने पर \(-3x\ge 9\), फिर (-3) से भाग देने पर \(x\le -3\)। ऋणात्मक भाग के बाद चिह्न पलटता है।
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असमानता (x+1<2x-5) का हल क्या है?
What is the solution of the inequality (x+1<2x-5)?
#linear inequalities
#variables both sides
#greater result
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A (x>6)
B (x<6)
C \(x\ge 6\)
D \(x\le 6\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (x) from both sides gives (1<x-5), so (x>6). Write the final direction of (x) clearly.
Step 2
Why this answer is correct
The correct answer is A. (x>6). Subtracting (x) from both sides gives (1<x-5), so (x>6). Write the final direction of (x) clearly.
Step 3
Exam Tip
दोनों पक्षों से (x) घटाने पर (1<x-5), इसलिए (x>6)। अंतिम उत्तर में (x) की दिशा स्पष्ट लिखें।
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असमानता (3x-4>2x+1) का हल क्या है?
What is the solution of the inequality (3x-4>2x+1)?
#linear inequalities
#variables both sides
#transposition
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A (x>5)
B (x<5)
C \(x\ge 5\)
D \(x\le 5\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (2x) gives (x-4>1), so (x>5). Removing the smaller variable term is a simple method.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Subtracting (2x) gives (x-4>1), so (x>5). Removing the smaller variable term is a simple method.
Step 3
Exam Tip
(2x) घटाने पर (x-4>1), इसलिए (x>5)। छोटे चर पद को हटाना सरल तरीका है।
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असमानता \(8\ge x+3\) का हल क्या है?
What is the solution of the inequality \(8\ge x+3\)?
#linear inequalities
#rewrite solution
#less than equal
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A \(x\le 5\)
B \(x\ge 5\)
C (x<5)
D (x>5)
Explanation opens after your attempt
Correct Answer
A. \(x\le 5\)
Step 1
Concept
Subtracting (3) gives \(5\ge x\), that is \(x\le 5\). Preserve the sign direction while changing form.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 5\). Subtracting (3) gives \(5\ge x\), that is \(x\le 5\). Preserve the sign direction while changing form.
Step 3
Exam Tip
(3) घटाने पर \(5\ge x\), अर्थात \(x\le 5\)। रूप बदलते समय चिह्न की दिशा सुरक्षित रखें।
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असमानता (11<2x+1) का हल क्या है?
What is the solution of the inequality (11<2x+1)?
#linear inequalities
#rewrite solution
#greater than
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A (x>5)
B (x<5)
C \(x\ge 5\)
D \(x\le 5\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (1) gives (10<2x), so (5<x), meaning (x>5). Read the sign correctly when writing (x) on the left.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Subtracting (1) gives (10<2x), so (5<x), meaning (x>5). Read the sign correctly when writing (x) on the left.
Step 3
Exam Tip
(1) घटाने पर (10<2x), इसलिए (5<x) यानी (x>5)। (x) को दाईं ओर से बाईं ओर लिखते समय चिह्न पलटकर पढ़ें।
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असमानता \(2(x+3)\le x+10\) का हल क्या है?
What is the solution of the inequality \(2(x+3)\le x+10\)?
#linear inequalities
#brackets
#variables both sides
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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
A. \(x\le 4\)
Step 1
Concept
From \(2x+6\le x+10\), we get \(x\le 4\). Open brackets and combine like terms.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 4\). From \(2x+6\le x+10\), we get \(x\le 4\). Open brackets and combine like terms.
Step 3
Exam Tip
\(2x+6\le x+10\) से \(x\le 4\) मिलता है। कोष्ठक खोलकर समान पदों को मिलाएं।
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असमानता (3(x-1)>x+5) का हल क्या है?
What is the solution of the inequality (3(x-1)>x+5)?
#linear inequalities
#brackets
#strict inequality
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A (x>4)
B (x<4)
C \(x\ge 4\)
D \(x\le 4\)
Explanation opens after your attempt
Step 1
Concept
From (3x-3>x+5), we get (2x>8), so (x>4). Handle the minus sign inside brackets carefully.
Step 2
Why this answer is correct
The correct answer is A. (x>4). From (3x-3>x+5), we get (2x>8), so (x>4). Handle the minus sign inside brackets carefully.
Step 3
Exam Tip
(3x-3>x+5) से (2x>8), इसलिए (x>4)। कोष्ठक में ऋण चिह्न को ध्यान से संभालें।
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असमानता \(\frac{x+2}{3}<5\) का हल क्या है?
What is the solution of the inequality \(\frac{x+2}{3}<5\)?
#linear inequalities
#fraction
#positive denominator
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A (x<13)
B (x>13)
C \(x\le 13\)
D \(x\ge 13\)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (3) gives (x+2<15), so (x<13). Multiplying by a positive denominator does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<13). Multiplying by (3) gives (x+2<15), so (x<13). Multiplying by a positive denominator does not change the sign.
Step 3
Exam Tip
(3) से गुणा करने पर (x+2<15), इसलिए (x<13)। धनात्मक हर से गुणा करने पर चिह्न नहीं बदलता।
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असमानता \(\frac{3x-2}{2}\ge 5\) का हल क्या है?
What is the solution of the inequality \(\frac{3x-2}{2}\ge 5\)?
#linear inequalities
#fraction
#two step
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A \(x\ge 4\)
B \(x\le 4\)
C (x>4)
D (x<4)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
Multiplying by (2) gives \(3x-2\ge 10\), so \(x\ge 4\). Remove the fraction to form a simple linear inequality.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). Multiplying by (2) gives \(3x-2\ge 10\), so \(x\ge 4\). Remove the fraction to form a simple linear inequality.
Step 3
Exam Tip
(2) से गुणा करने पर \(3x-2\ge 10\), इसलिए \(x\ge 4\)। भिन्न हटाकर सरल रैखिक असमानता बनाएं।
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यदि (x) एक पूर्ण संख्या है और \(x\le 3\), तो हल समुच्चय क्या है?
If (x) is a whole number and \(x\le 3\), what is the solution set?
#linear inequalities
#whole numbers
#solution set
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A \({0,1,2,3}\)
B \({1,2,3}\)
C \({0,1,2}\)
D \({3,4,5}\)
Explanation opens after your attempt
Correct Answer
A. \({0,1,2,3}\)
Step 1
Concept
Whole numbers start from (0), so (0,1,2,3) are included. Because of \(\le\), (3) is also included.
Step 2
Why this answer is correct
The correct answer is A. \({0,1,2,3}\). Whole numbers start from (0), so (0,1,2,3) are included. Because of \(\le\), (3) is also included.
Step 3
Exam Tip
पूर्ण संख्याएं (0) से शुरू होती हैं, इसलिए (0,1,2,3) शामिल हैं। \(\le\) के कारण (3) भी शामिल है।
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असमानता (x-7>-2) का हल क्या है?
What is the solution of the inequality (x-7>-2)?
#linear inequalities
#addition
#negative constant
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A (x>5)
B (x<5)
C \(x\ge 5\)
D \(x\le 5\)
Explanation opens after your attempt
Step 1
Concept
Adding (7) to both sides gives (x>5). Addition or subtraction does not change the inequality sign.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Adding (7) to both sides gives (x>5). Addition or subtraction does not change the inequality sign.
Step 3
Exam Tip
दोनों पक्षों में (7) जोड़ने पर (x>5) मिलता है। जोड़ या घटाव में असमानता का चिह्न नहीं बदलता।
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असमानता \(x+6\le -1\) का हल क्या है?
What is the solution of the inequality \(x+6\le -1\)?
#linear inequalities
#negative numbers
#subtraction
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A \(x\le -7\)
B \(x\ge -7\)
C (x<-7)
D (x>-7)
Explanation opens after your attempt
Correct Answer
A. \(x\le -7\)
Step 1
Concept
Subtracting (6) from both sides gives \(x\le -7\). Even with a negative answer, addition or subtraction does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le -7\). Subtracting (6) from both sides gives \(x\le -7\). Even with a negative answer, addition or subtraction does not change the sign.
Step 3
Exam Tip
दोनों पक्षों से (6) घटाने पर \(x\le -7\)। ऋणात्मक उत्तर आने पर भी जोड़-घटाव से चिह्न नहीं बदलता।
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असमानता (-4x<16) का हल क्या है?
What is the solution of the inequality (-4x<16)?
#linear inequalities
#negative coefficient
#common mistake
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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 (-4) reverses the sign and gives (x>-4). A negative coefficient is the most common mistake.
Step 2
Why this answer is correct
The correct answer is A. (x>-4). Dividing by (-4) reverses the sign and gives (x>-4). A negative coefficient is the most common mistake.
Step 3
Exam Tip
(-4) से भाग देने पर चिह्न पलटता है और (x>-4) मिलता है। ऋणात्मक गुणांक सबसे आम गलती है।
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असमानता \(6-2x\ge 0\) का हल क्या है?
What is the solution of the inequality \(6-2x\ge 0\)?
#linear inequalities
#zero comparison
#sign reversal
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A \(x\le 3\)
B \(x\ge 3\)
C (x<3)
D (x>3)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
We get \(-2x\ge -6\), so division by (-2) gives \(x\le 3\). Reverse the sign while dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). We get \(-2x\ge -6\), so division by (-2) gives \(x\le 3\). Reverse the sign while dividing by a negative number.
Step 3
Exam Tip
\(-2x\ge -6\), इसलिए (-2) से भाग देने पर \(x\le 3\)। ऋणात्मक से भाग देते समय चिह्न पलटें।
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असमानता (7x+2<3x+18) का हल क्या है?
What is the solution of the inequality (7x+2<3x+18)?
#linear inequalities
#variables both sides
#easy
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A (x<4)
B (x>4)
C \(x\le 4\)
D \(x\ge 4\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (3x) gives (4x+2<18), so (x<4). First bring variable terms to one side.
Step 2
Why this answer is correct
The correct answer is A. (x<4). Subtracting (3x) gives (4x+2<18), so (x<4). First bring variable terms to one side.
Step 3
Exam Tip
(3x) घटाने पर (4x+2<18), इसलिए (x<4)। पहले चर पदों को एक तरफ लाएं।
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असमानता \(9x-5\ge 4x+20\) का हल क्या है?
What is the solution of the inequality \(9x-5\ge 4x+20\)?
#linear inequalities
#variables both sides
#greater equal
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A \(x\ge 5\)
B \(x\le 5\)
C (x>5)
D (x<5)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 5\)
Step 1
Concept
Subtracting (4x) and adding (5) gives \(5x\ge 25\), so \(x\ge 5\). Keep the equality part till the end.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 5\). Subtracting (4x) and adding (5) gives \(5x\ge 25\), so \(x\ge 5\). Keep the equality part till the end.
Step 3
Exam Tip
(4x) घटाने और (5) जोड़ने पर \(5x\ge 25\), इसलिए \(x\ge 5\)। बराबरी का चिह्न अंत में भी रखें।
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रवि के पास (x) रुपये हैं। यदि \(x+15\ge 50\), तो (x) का न्यूनतम मान क्या है?
Ravi has (x) rupees. If \(x+15\ge 50\), what is the minimum value of (x)?
#linear inequalities
#word problem
#minimum value
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A (35)
B (34)
C (50)
D (65)
Explanation opens after your attempt
Step 1
Concept
Subtracting (15) gives \(x\ge 35\), so the minimum value is (35). In a word problem, form the inequality first.
Step 2
Why this answer is correct
The correct answer is A. (35). Subtracting (15) gives \(x\ge 35\), so the minimum value is (35). In a word problem, form the inequality first.
Step 3
Exam Tip
(15) घटाने पर \(x\ge 35\), इसलिए न्यूनतम मान (35) है। शब्द प्रश्न में भी पहले असमानता बनाएं।
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किसी संख्या (x) का दुगुना (14) से कम है। (x) के लिए सही असमानता और हल क्या है?
Twice a number (x) is less than (14). What is the correct inequality and solution for (x)?
#linear inequalities
#word problem
#translation
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A (2x<14,\ x<7)
B (2x>14,\ x>7)
C (x+2<14,\ x<12)
D \(2x\le 14,\ x\le 7\)
Explanation opens after your attempt
Correct Answer
A. (2x<14,\ x<7)
Step 1
Concept
Twice means (2x) and less than means (<), so (2x<14) and (x<7). Convert words into the correct mathematical sign.
Step 2
Why this answer is correct
The correct answer is A. (2x<14,\ x<7). Twice means (2x) and less than means (<), so (2x<14) and (x<7). Convert words into the correct mathematical sign.
Step 3
Exam Tip
दुगुना का अर्थ (2x) है और कम है का अर्थ (<) है, इसलिए (2x<14) और (x<7)। शब्दों को सही गणितीय चिह्न में बदलें।
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असमानता \(2x-9\ge 1\) का हल क्या है?
What is the solution of the inequality \(2x-9\ge 1\)?
#linear inequalities
#one variable
#algebraic solution
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A \(x\ge 5\)
B \(x\le 5\)
C (x>5)
D (x<5)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 5\)
Step 1
Concept
Adding (9) to both sides gives \(2x\ge 10\), so \(x\ge 5\). Dividing by a positive number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 5\). Adding (9) to both sides gives \(2x\ge 10\), so \(x\ge 5\). Dividing by a positive number does not change the sign.
Step 3
Exam Tip
दोनों पक्षों में (9) जोड़ने पर \(2x\ge 10\), इसलिए \(x\ge 5\)। धनात्मक संख्या से भाग देने पर चिह्न नहीं बदलता।
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असमानता \(\frac{x-4}{6}\le 2\) का हल क्या है?
What is the solution of the inequality \(\frac{x-4}{6}\le 2\)?
#linear inequalities
#fraction
#less than equal
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A \(x\le 16\)
B \(x\ge 16\)
C (x<16)
D (x>16)
Explanation opens after your attempt
Correct Answer
A. \(x\le 16\)
Step 1
Concept
Multiplying both sides by (6) gives \(x-4\le 12\), so \(x\le 16\). Multiplying by a positive denominator keeps the sign unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 16\). Multiplying both sides by (6) gives \(x-4\le 12\), so \(x\le 16\). Multiplying by a positive denominator keeps the sign unchanged.
Step 3
Exam Tip
दोनों पक्षों को (6) से गुणा करने पर \(x-4\le 12\), इसलिए \(x\le 16\)। धनात्मक हर से गुणा करने पर चिह्न वही रहता है।
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यदि (x) एक पूर्णांक है और (3x+2<17), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (3x+2<17), what is the greatest possible (x)?
#linear inequalities
#integer solution
#greatest integer
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A (4)
B (5)
C (6)
D (3)
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Step 1
Concept
The inequality gives (3x<15), so (x<5) and the greatest integer is (4). A strict inequality does not include the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives (3x<15), so (x<5) and the greatest integer is (4). A strict inequality does not include the boundary value.
Step 3
Exam Tip
असमानता से (3x<15), इसलिए (x<5) और सबसे बड़ा पूर्णांक (4) है। सख्त असमानता में सीमा मान शामिल नहीं होता।
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असमानता (2(x+4)>x+13) का हल क्या है?
What is the solution of the inequality (2(x+4)>x+13)?
#linear inequalities
#brackets
#variables both sides
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A (x>5)
B (x<5)
C \(x\ge 5\)
D \(x\le 5\)
Explanation opens after your attempt
Step 1
Concept
Opening brackets gives (2x+8>x+13), so (x>5). Multiply each term correctly while opening brackets.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Opening brackets gives (2x+8>x+13), so (x>5). Multiply each term correctly while opening brackets.
Step 3
Exam Tip
कोष्ठक खोलने पर (2x+8>x+13), इसलिए (x>5)। कोष्ठक खोलते समय प्रत्येक पद से गुणा करें।
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असमानता (4x+7<2x+19) का हल क्या है?
What is the solution of the inequality (4x+7<2x+19)?
#linear inequalities
#one variable
#variables both sides
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A (x<6)
B (x>6)
C \(x\le 6\)
D \(x\ge 6\)
Explanation opens after your attempt
Step 1
Concept
Subtracting (2x) from both sides gives (2x+7<19), so (x<6). Keeping variable terms on one side makes the solution faster.
Step 2
Why this answer is correct
The correct answer is A. (x<6). Subtracting (2x) from both sides gives (2x+7<19), so (x<6). Keeping variable terms on one side makes the solution faster.
Step 3
Exam Tip
दोनों पक्षों से (2x) घटाने पर (2x+7<19), इसलिए (x<6)। चर पदों को एक तरफ रखने से हल जल्दी मिलता है।
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