यदि \(x\in\mathbb{Z}\) और (2x+1<8), तो संख्या रेखा पर सबसे बड़ा marked integer कौन-सा होगा?
If \(x\in\mathbb{Z}\) and (2x+1<8), what is the greatest marked integer on the number line?
#linear inequalities
#integer solution
#number line
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(2x<7) gives \(x<\frac{7}{2}\), so the greatest integer is (3). In exams, choose the integer just before the boundary.
Step 2
Why this answer is correct
The correct answer is B. (3). (2x<7) gives \(x<\frac{7}{2}\), so the greatest integer is (3). In exams, choose the integer just before the boundary.
Step 3
Exam Tip
(2x<7) से \(x<\frac{7}{2}\), इसलिए सबसे बड़ा integer (3) है। परीक्षा में integer answer में boundary से पहले वाला पूर्णांक लें।
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अंतराल ([5,12)) में कौन सा पूर्णांक सबसे बड़ा सदस्य है?
Which integer is the greatest member of the interval ([5,12))?
#linear-inequalities
#integer-solution
#number-line
A (12)
B (13)
C (11)
D (5)
Explanation opens after your attempt
Step 1
Concept
(12) is not included, so the greatest integer before it is (11). Do not take the open right endpoint as the answer.
Step 2
Why this answer is correct
The correct answer is C. (11). (12) is not included, so the greatest integer before it is (11). Do not take the open right endpoint as the answer.
Step 3
Exam Tip
(12) शामिल नहीं है इसलिए उससे पहले का सबसे बड़ा पूर्णांक (11) होगा। खुले दाएँ सिरे को उत्तर न मानें।
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अंतराल ([-2,4)) में कौन सा पूर्णांक सबसे बड़ा सदस्य है?
Which integer is the greatest member of the interval ([-2,4))?
#linear-inequalities
#integer-solution
#number-line
A (4)
B (5)
C (3)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(4) is not included, so the greatest integer before it is (3). Do not take the open right endpoint as the answer.
Step 2
Why this answer is correct
The correct answer is C. (3). (4) is not included, so the greatest integer before it is (3). Do not take the open right endpoint as the answer.
Step 3
Exam Tip
(4) शामिल नहीं है इसलिए उससे पहले का सबसे बड़ा पूर्णांक (3) होगा। खुले दाएँ सिरे को उत्तर में न लें।
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यदि \(x\in \mathbb{Z}\), \( \frac{2x-7}{3}<5 \) और \( 4-\frac{x}{2}\leq 1 \), तो (x) के कितने पूर्णांक मान संभव हैं?
If \(x\in \mathbb{Z}\), \( \frac{2x-7}{3}<5 \), and \( 4-\frac{x}{2}\leq 1 \), how many integer values of (x) are possible?
#integer solution
#system inequalities
#expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The first inequality gives (x<11), and the second gives \(x\geq 6\). The integers are (6,7,8,9,10), so there are (5) values.
Step 2
Why this answer is correct
The correct answer is A. (5). The first inequality gives (x<11), and the second gives \(x\geq 6\). The integers are (6,7,8,9,10), so there are (5) values.
Step 3
Exam Tip
पहली असमानता से (x<11) और दूसरी से \(x\geq 6\) मिलता है। पूर्णांक (6,7,8,9,10) हैं, इसलिए कुल (5) मान हैं।
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यदि \( \frac{2x-3}{4}\geq \frac{x+5}{6} \), तो सबसे छोटा पूर्णांक (x) क्या होगा?
If \( \frac{2x-3}{4}\geq \frac{x+5}{6} \), what is the smallest integer (x)?
#integer solution
#fraction inequality
#expert
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (12) gives \(6x-9\geq 2x+10\) and \(x\geq \frac{19}{4}\). Therefore the smallest integer is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). Multiplying by (12) gives \(6x-9\geq 2x+10\) and \(x\geq \frac{19}{4}\). Therefore the smallest integer is (7).
Step 3
Exam Tip
(12) से गुणा करने पर \(6x-9\geq 2x+10\) और \(x\geq \frac{19}{4}\) मिलता है। इसलिए सबसे छोटा पूर्णांक (7) है।
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असमीका (-4x+6<-10) को संतुष्ट करने वाला सबसे छोटा पूर्णांक (x) क्या है?
What is the least integer (x) satisfying (-4x+6<-10)?
#linear inequalities
#integer solution
#least integer
A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
(-4x<-16) gives (x>4), so the least integer is (5). Do not include the boundary in a strict inequality.
Step 2
Why this answer is correct
The correct answer is B. (5). (-4x<-16) gives (x>4), so the least integer is (5). Do not include the boundary in a strict inequality.
Step 3
Exam Tip
(-4x<-16) से (x>4), इसलिए सबसे छोटा पूर्णांक (5) है। परीक्षा में सख्त असमीका में सीमा को शामिल न करें।
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असमीका (5x+4<31) को संतुष्ट करने वाला सबसे बड़ा पूर्णांक (x) क्या है?
What is the greatest integer (x) satisfying (5x+4<31)?
#linear inequalities
#integer solution
#greatest integer
A (5)
B (6)
C (4)
D (7)
Explanation opens after your attempt
Step 1
Concept
(5x<27) gives \(x<\frac{27}{5}\), so the greatest integer is (5). Check integers near the boundary.
Step 2
Why this answer is correct
The correct answer is A. (5). (5x<27) gives \(x<\frac{27}{5}\), so the greatest integer is (5). Check integers near the boundary.
Step 3
Exam Tip
(5x<27) से \(x<\frac{27}{5}\), इसलिए सबसे बड़ा पूर्णांक (5) है। परीक्षा में सीमा के पास वाले पूर्णांक जांचें।
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असमीका \(-3x+10\le 1\) को संतुष्ट करने वाला सबसे छोटा पूर्णांक (x) क्या है?
What is the least integer (x) satisfying \(-3x+10\le 1\)?
#linear inequalities
#integer solution
#least integer
A (2)
B (3)
C (4)
D (-3)
Explanation opens after your attempt
Step 1
Concept
\(-3x\le -9\) gives \(x\ge 3\), so the least integer is (3). Check the boundary after division by a negative.
Step 2
Why this answer is correct
The correct answer is B. (3). \(-3x\le -9\) gives \(x\ge 3\), so the least integer is (3). Check the boundary after division by a negative.
Step 3
Exam Tip
\(-3x\le -9\) से \(x\ge 3\), इसलिए सबसे छोटा पूर्णांक (3) है। परीक्षा में ऋणात्मक भाग देने के बाद सीमा जांचें।
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असमीका (4x-3<18) को संतुष्ट करने वाला सबसे बड़ा पूर्णांक (x) क्या है?
What is the greatest integer (x) satisfying (4x-3<18)?
#linear inequalities
#integer solution
#greatest integer
A (5)
B (6)
C (4)
D (7)
Explanation opens after your attempt
Step 1
Concept
(4x<21) gives \(x<\frac{21}{4}\), so the greatest integer is (5). When an integer answer is asked, check values near the boundary.
Step 2
Why this answer is correct
The correct answer is A. (5). (4x<21) gives \(x<\frac{21}{4}\), so the greatest integer is (5). When an integer answer is asked, check values near the boundary.
Step 3
Exam Tip
(4x<21) से \(x<\frac{21}{4}\), इसलिए सबसे बड़ा पूर्णांक (5) है। परीक्षा में पूर्णांक उत्तर मांगने पर सीमा के पास जांच करें।
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असमानता \(11x+6\geq 7x+34\) और (x) पूर्णांक है। सबसे छोटा संभव (x) क्या है?
For \(11x+6\geq 7x+34\) and integer (x), what is the least possible (x)?
#integer solution
#least value
#linear inequality
A (8)
B (7)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
From \(4x\geq 28\), we get \(x\geq 7\). Hence the least integer solution is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). From \(4x\geq 28\), we get \(x\geq 7\). Hence the least integer solution is (7).
Step 3
Exam Tip
\(4x\geq 28\) से \(x\geq 7\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (7) है।
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यदि (x) पूर्णांक है और \(-3\leq x<4\), तो हल समुच्चय कौन सा है?
If (x) is an integer and \(-3\leq x<4\), which is the solution set?
#integer solution
#compound inequality
#set
A ({-2,-1,0,1,2,3})
B ({-3,-2,-1,0,1,2,3,4})
C ({-3,-2,-1,0,1,2,3})
D ({-3,-2,-1,0,1,2})
Explanation opens after your attempt
Correct Answer
C. ({-3,-2,-1,0,1,2,3})
Step 1
Concept
(-3) is included and (4) is not included. Therefore the integer solutions are ({-3,-2,-1,0,1,2,3}).
Step 2
Why this answer is correct
The correct answer is C. ({-3,-2,-1,0,1,2,3}). (-3) is included and (4) is not included. Therefore the integer solutions are ({-3,-2,-1,0,1,2,3}).
Step 3
Exam Tip
(-3) शामिल है और (4) शामिल नहीं है। इसलिए पूर्णांक हल ({-3,-2,-1,0,1,2,3}) हैं।
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यदि (x) पूर्णांक है और (4x-3<21), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (4x-3<21), what is the greatest possible (x)?
#integer solution
#greatest integer
#linear inequality
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (4x<24), we get (x<6). The greatest integer less than (6) is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). From (4x<24), we get (x<6). The greatest integer less than (6) is (5).
Step 3
Exam Tip
(4x<24) से (x<6) मिलता है। (6) से छोटा सबसे बड़ा पूर्णांक (5) है।
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असमानता \(7x-4\geq 3x+20\) और (x) पूर्णांक है। सबसे छोटा संभव (x) क्या है?
For \(7x-4\geq 3x+20\) and integer (x), what is the least possible (x)?
#integer solution
#least value
#linear inequality
A (6)
B (5)
C (7)
D (4)
Explanation opens after your attempt
Step 1
Concept
From \(4x\geq 24\), we get \(x\geq 6\). Hence the least integer solution is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). From \(4x\geq 24\), we get \(x\geq 6\). Hence the least integer solution is (6).
Step 3
Exam Tip
\(4x\geq 24\) से \(x\geq 6\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (6) है।
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यदि (x) एक पूर्णांक है और (2x+1<9), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (2x+1<9), what is the greatest possible (x)?
#integer solution
#greatest integer
#inequality
A (3)
B (4)
C (5)
D (2)
Explanation opens after your attempt
Step 1
Concept
From (2x<8), we get (x<4). The greatest integer less than (4) is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). From (2x<8), we get (x<4). The greatest integer less than (4) is (3).
Step 3
Exam Tip
(2x<8) से (x<4) मिलता है। (4) से छोटा सबसे बड़ा पूर्णांक (3) है।
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यदि (x) एक पूर्णांक है और \(4x-1\le 15\), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and \(4x-1\le 15\), what is the greatest possible (x)?
#linear inequalities
#integer solution
#greatest integer
A (4)
B (3)
C (5)
D (15)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(4x\le 16\), so \(x\le 4\) and the greatest integer is (4). The sign \(\le\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives \(4x\le 16\), so \(x\le 4\) and the greatest integer is (4). The sign \(\le\) includes the boundary value.
Step 3
Exam Tip
असमानता से \(4x\le 16\), इसलिए \(x\le 4\) और सबसे बड़ा पूर्णांक (4) है। \(\le\) में सीमा मान शामिल होता है।
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यदि (x) एक पूर्णांक है और \(3x\ge 24\), तो सबसे छोटा संभव (x) क्या है?
If (x) is an integer and \(3x\ge 24\), what is the least possible (x)?
#linear inequalities
#integer solution
#least integer
A (8)
B (7)
C (9)
D (24)
Explanation opens after your attempt
Step 1
Concept
Dividing by (3) gives \(x\ge 8\), so the least integer is (8). The sign \(\ge\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. (8). Dividing by (3) gives \(x\ge 8\), so the least integer is (8). The sign \(\ge\) includes the boundary value.
Step 3
Exam Tip
(3) से भाग देने पर \(x\ge 8\), इसलिए सबसे छोटा पूर्णांक (8) है। \(\ge\) सीमा मान को शामिल करता है।
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यदि (x) एक पूर्णांक है और (x+6<11), तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and (x+6<11), what is the greatest possible (x)?
#linear inequalities
#integer solution
#greatest integer
A (4)
B (5)
C (6)
D (11)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x<5), so the greatest integer is (4). A strict sign does not include the boundary.
Step 2
Why this answer is correct
The correct answer is A. (4). The inequality gives (x<5), so the greatest integer is (4). A strict sign does not include the boundary.
Step 3
Exam Tip
असमानता से (x<5) मिलता है, इसलिए सबसे बड़ा पूर्णांक (4) है। सख्त चिह्न में सीमा शामिल नहीं होती।
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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
A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
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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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
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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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
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 \(x\in \mathbb{N}\) और (2x+1<12), तो सबसे बड़ा संभव (x) क्या है?
If \(x\in \mathbb{N}\) and (2x+1<12), what is the greatest possible (x)?
#natural numbers
#integer solution
#upper bound
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(2x<11) gives \(x<\frac{11}{2}\), so the greatest natural number is (x=5). For integer domains, do not write a decimal answer.
Step 2
Why this answer is correct
The correct answer is B. (5). (2x<11) gives \(x<\frac{11}{2}\), so the greatest natural number is (x=5). For integer domains, do not write a decimal answer.
Step 3
Exam Tip
(2x<11) से \(x<\frac{11}{2}\) है इसलिए प्राकृतिक संख्याओं में सबसे बड़ा (x=5) है। पूर्णांक सीमा में दशमलव उत्तर नहीं लिखते।
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यदि \(x\in\mathbb{Z}\) और \(\frac{x-2}{3}\leq -1\) है तो सबसे बड़ा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and \(\frac{x-2}{3}\leq -1\), what is the greatest possible (x)?
#integer-solution
#fractional-inequality
#greatest-value
A (1)
B (0)
C (-1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (3) gives \(x-2\leq -3\), so \(x\leq -1\). Therefore the greatest integer solution is (-1).
Step 2
Why this answer is correct
The correct answer is C. (-1). Multiplying by (3) gives \(x-2\leq -3\), so \(x\leq -1\). Therefore the greatest integer solution is (-1).
Step 3
Exam Tip
(3) से गुणा करने पर \(x-2\leq -3\) और \(x\leq -1\) मिलता है। इसलिए सबसे बड़ा पूर्णांक हल (-1) है।
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यदि \(x\in\mathbb{Z}\) और \(-3\leq \frac{x}{2}<4\) है तो हल समुच्चय कौन सा है?
If \(x\in\mathbb{Z}\) and \(-3\leq \frac{x}{2}<4\), what is the solution set?
#integer-solution
#compound-fraction
#solution-set
A ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7})
B ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8})
C ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8})
D ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7})
Step 1
Concept
Multiplying by (2) gives \(-6\leq x<8\). Therefore the integer solutions are from (-6) to (7).
Step 2
Why this answer is correct
The correct answer is A. ({-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}). Multiplying by (2) gives \(-6\leq x<8\). Therefore the integer solutions are from (-6) to (7).
Step 3
Exam Tip
(2) से गुणा करने पर \(-6\leq x<8\) मिलता है। इसलिए पूर्णांक हल (-6) से (7) तक हैं।
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यदि \(x\in\mathbb{Z}\) और \(3x+2\geq 17\) है तो सबसे छोटा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and \(3x+2\geq 17\), what is the least possible (x)?
#least-integer
#integer-solution
#linear-inequality
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(3x\geq 15\), so \(x\geq 5\). Therefore the least integer solution is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). The inequality gives \(3x\geq 15\), so \(x\geq 5\). Therefore the least integer solution is (5).
Step 3
Exam Tip
असमता से \(3x\geq 15\) और \(x\geq 5\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (5) है।
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यदि \(x\in\mathbb{Z}\) और (4x+9<1) है तो सबसे बड़ा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and (4x+9<1), what is the greatest possible (x)?
#integer-solution
#greatest-value
#strict-inequality
A (0)
B (-1)
C (-2)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (4x<-8), so (x<-2). The greatest integer less than (-2) is (-3).
Step 2
Why this answer is correct
The correct answer is C. (-2). The inequality gives (4x<-8), so (x<-2). The greatest integer less than (-2) is (-3).
Step 3
Exam Tip
असमता से (4x<-8) इसलिए (x<-2) मिलता है। सबसे बड़ा पूर्णांक हल (-3) नहीं बल्कि (-3) से पहले जांचें और सही मान (-3) होगा।
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यदि \(x\in\mathbb{Z}\) और \(\frac{x+5}{2}>3\) है तो सबसे छोटा संभव (x) क्या है?
If \(x\in\mathbb{Z}\) and \(\frac{x+5}{2}>3\), what is the least possible (x)?
#integer-solution
#fractional-inequality
#least-value
A (2)
B (1)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
Multiplying by (2) gives (x+5>6), so (x>1). For integer solutions, the least value is (2).
Step 2
Why this answer is correct
The correct answer is A. (2). Multiplying by (2) gives (x+5>6), so (x>1). For integer solutions, the least value is (2).
Step 3
Exam Tip
(2) से गुणा करने पर (x+5>6) और (x>1) मिलता है। पूर्णांक हल में सबसे छोटा मान (2) होगा।
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यदि (x) एक पूर्णांक है और \(2x-5\leq 9\) है तो सबसे बड़ा संभव (x) क्या है?
If (x) is an integer and \(2x-5\leq 9\), what is the greatest possible (x)?
#integer-solution
#greatest-value
#linear-inequality
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The inequality gives \(2x\leq 14\), so \(x\leq 7\). With an integer restriction, choose an integer final answer.
Step 2
Why this answer is correct
The correct answer is B. (7). The inequality gives \(2x\leq 14\), so \(x\leq 7\). With an integer restriction, choose an integer final answer.
Step 3
Exam Tip
असमता से \(2x\leq 14\) इसलिए \(x\leq 7\) मिलता है। पूर्णांक प्रतिबंध हो तो अंतिम उत्तर पूर्णांक ही लें।
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यदि \(2x-1\ge 7\) है तो (x) का न्यूनतम पूर्णांक मान क्या है?
If \(2x-1\ge 7\) then what is the least integer value of (x)?
#linear-inequalities
#integer-solution
#least-value
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The solution is \(2x\ge 8\) so \(x\ge 4\) and the least integer is (4). First find the real solution and then choose the integer.
Step 2
Why this answer is correct
The correct answer is B. (4). The solution is \(2x\ge 8\) so \(x\ge 4\) and the least integer is (4). First find the real solution and then choose the integer.
Step 3
Exam Tip
हल \(2x\ge 8\) यानी \(x\ge 4\) है इसलिए न्यूनतम पूर्णांक (4) है। पहले वास्तविक हल निकालें फिर पूर्णांक चुनें।
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