compound inequality se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
116 questions tagged with compound inequality.
What is the integer solution set of \(-3\leq 2x+1<7\)?
A. ({-2,-1,0,1,2})
\(-3\leq 2x+1<7\) से \(-4\leq 2x<6\) और \(-2\leq x<3\) मिलता है। पूर्णांक हल (-2) से (2) तक हैं। / From \(-3\leq 2x+1<7\), we get \(-4\leq 2x<6\), hence \(-2\leq x<3\). The integer solutions are from (-2) to (2).
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If \(x\in\mathbb{R}\) and \(12<4x\leq 28\), which solution is correct?
A. \(3<x\leq 7\)
(4) से भाग देने पर \(3<x\leq 7\) मिलता है। धनात्मक संख्या से भाग देने पर चिन्ह नहीं बदलता। / Dividing by (4) gives \(3<x\leq 7\). Dividing by a positive number does not change the signs.
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If \(x\in\mathbb{Z}\) and \(-10<2x\leq 6\), how many integer solutions are there?
B. (8)
भाग देने पर \(-5<x\leq 3\) मिलता है। पूर्णांक हल (-4,-3,-2,-1,0,1,2,3) हैं इसलिए कुल (8) हैं। / Dividing gives \(-5<x\leq 3\). The integer solutions are (-4,-3,-2,-1,0,1,2,3), so there are (8).
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Which value is not a solution of \(-4<x\leq 3\)?
D. (x=-4)
(-4) खुला सिरा है इसलिए (x=-4) शामिल नहीं है। सीमा मान जांचना ऐसे प्रश्नों में जरूरी है। / (-4) is an open endpoint, so (x=-4) is not included. Checking boundary values is essential in such questions.
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If \(-9\leq 3x-6<12\), which interval for (x) is correct?
A. ([-1,6))
(6) जोड़ने पर \(-3\leq 3x<18\) और फिर \(-1\leq x<6\) मिलता है। संयुक्त असमता में दोनों ओर समान क्रिया करें। / Adding (6) gives \(-3\leq 3x<18\), then \(-1\leq x<6\). Apply the same operation to all parts of a compound inequality.
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If \(x\in\mathbb{Z}\) and \(1\leq 2x-1<9\), what is the solution set?
A. ({1,2,3,4})
\(1\leq 2x-1<9\) से \(2\leq 2x<10\) और \(1\leq x<5\) मिलता है। पूर्णांक हल (1) से (4) तक हैं। / From \(1\leq 2x-1<9\), we get \(2\leq 2x<10\), hence \(1\leq x<5\). The integer solutions are (1) through (4).
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Which value is a solution of \(-3\leq x<1\)?
A. (x=-3)
(-3) शामिल है क्योंकि \(\leq\) है और (1) शामिल नहीं है क्योंकि (<) है। खुले और बंद सिरों को अलग-अलग जांचें। / (-3) is included because of \(\leq\), while (1) is not included because of (<). Check open and closed endpoints separately.
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Which option includes (x=2) in the solution but excludes (x=6)?
A. \(2\leq x<6\)
\(2\leq x<6\) में (2) शामिल है और (6) शामिल नहीं है। समावेशन के लिए बराबरी का चिन्ह देखें। / In \(2\leq x<6\), (2) is included and (6) is excluded. Check the equality sign for inclusion.
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If (2x+3) is less than (11) and greater than (1), what is the solution for (x)?
A. (-1<x<4)
(1<2x+3<11) से (-2<2x<8) और (-1<x<4) मिलता है। वाक्य को पहले संयुक्त असमता में बदलें। / From (1<2x+3<11), we get (-2<2x<8), hence (-1<x<4). First convert the statement into a compound inequality.
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Which option is the correct interval form of (x<-1) or \(x\geq 4\)?
A. (\(-\infty,-1\)\cup[4,\infty))
या का अर्थ दोनों हलों का संघ है। खुले और बंद सिरों को असमता के चिन्ह से मिलाएं। / Or means the union of the two solution sets. Match open and closed endpoints with the inequality signs.
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If \(x\in\mathbb{R}\) and \(0\leq 4x-8<12\), what is the interval for (x)?
A. ([2,5))
\(0\leq 4x-8<12\) से \(8\leq 4x<20\) और \(2\leq x<5\) मिलता है। संयुक्त असमता में दोनों सिरों को साथ-साथ हल करें। / From \(0\leq 4x-8<12\), we get \(8\leq 4x<20\), hence \(2\leq x<5\). Solve both ends of a compound inequality together.
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If \(x\in\mathbb{Z}\) and \(-1<2x+3\leq 9\), what is the solution set?
A. ({-1,0,1,2,3})
\(-1<2x+3\leq 9\) से \(-4<2x\leq 6\) और \(-2<x\leq 3\) मिलता है। पूर्णांक चुनते समय खुले और बंद सिरों का ध्यान रखें। / From \(-1<2x+3\leq 9\), we get \(-4<2x\leq 6\), hence \(-2<x\leq 3\). For integers, handle open and closed endpoints carefully.
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How do we write the interval ((-3,5]) as an inequality?
A. \(-3<x\le 5\)
((-3) बताता है कि (-3) शामिल नहीं है और (5]) बताता है कि (5) शामिल है। इसलिए \(-3<x\le 5\) सही है। / The symbol ((-3) shows that (-3) is not included and (5]) shows that (5) is included. Therefore \(-3<x\le 5\) is correct.
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B. \(12\le g\le 28\)
कम से कम (12) का अर्थ \(g\ge 12\) और अधिकतम (28) का अर्थ \(g\le 28\) है। दोनों को मिलाकर \(12\le g\le 28\) मिलता है। / At least (12) means \(g\ge 12\), and at most (28) means \(g\le 28\). Combining both gives \(12\le g\le 28\).
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If (x) is an integer and \(-4<x\le 1\), what are the values of (x)?
B. \(x\in{-3,-2,-1,0,1}\)
(-4) शामिल नहीं है पर (1) शामिल है। पूर्णांक मान (-3,-2,-1,0,1) होंगे। / The value (-4) is not included but (1) is included. The integer values are (-3,-2,-1,0,1).
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Which option correctly describes \(0\le x<10\)?
A. (x) (0) या उससे बड़ा और (10) से छोटा है(x) is (0) or more and less than (10)
\(0\le x<10\) में (0) शामिल है पर (10) शामिल नहीं है। संयुक्त असमानता को दोनों तरफ से पढ़ें। / In \(0\le x<10\), (0) is included but (10) is not included. Read a compound inequality from both sides.
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Which value is included in \(-1\le x<4\)?
C. (0)
(0) संख्या (-1) और (4) के बीच है। इस असमानता में (-1) शामिल है पर (4) शामिल नहीं है। / The number (0) lies between (-1) and (4). This inequality includes (-1) but excludes (4).
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How do we write the interval ([-4,2)) as an inequality?
B. \(-4\le x<2\)
([-4) बताता है कि (-4) शामिल है और (2)) बताता है कि (2) शामिल नहीं है। इसलिए \(-4\le x<2\) सही है। / The symbol ([-4) shows that (-4) is included and (2)) shows that (2) is not included. Therefore \(-4\le x<2\) is correct.
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B. \(20\le n\le 45\)
कम से कम (20) का अर्थ \(n\ge 20\) और अधिकतम (45) का अर्थ \(n\le 45\) है। दोनों को मिलाकर \(20\le n\le 45\) मिलता है। / At least (20) means \(n\ge 20\), and at most (45) means \(n\le 45\). Combining both gives \(20\le n\le 45\).
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Which option correctly describes \(3<x\le 8\)?
A. (x) (3) से बड़ा और (8) से छोटा या बराबर है(x) is greater than (3) and less than or equal to (8)
\(3<x\le 8\) में (3) शामिल नहीं है पर (8) शामिल है। संयुक्त असमानता को दोनों तरफ से पढ़ें। / In \(3<x\le 8\), (3) is not included but (8) is included. Read a compound inequality from both sides.
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B. \(25\le n\le 40\)
कम से कम (25) का अर्थ \(n\ge 25\) और अधिकतम (40) का अर्थ \(n\le 40\) है। दोनों को मिलाकर \(25\le n\le 40\) मिलता है। / At least (25) means \(n\ge 25\), and at most (40) means \(n\le 40\). Combining both gives \(25\le n\le 40\).
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How do we write the interval ((1,6]) as an inequality?
A. \(1<x\le 6\)
((1) बताता है कि (1) शामिल नहीं है और (6]) बताता है कि (6) शामिल है। इसलिए \(1<x\le 6\) सही है। / The symbol ((1) shows that (1) is not included and (6]) shows that (6) is included. Therefore \(1<x\le 6\) is correct.
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If (x) is an integer and \(-2<x\le 2\), what are the values of (x)?
B. \(x\in{-1,0,1,2}\)
(-2) शामिल नहीं है पर (2) शामिल है। पूर्णांक मान (-1,0,1,2) होंगे। / The value (-2) is not included, but (2) is included. The integer values are (-1,0,1,2).
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Which option correctly describes \(2\le x<5\)?
C. (x) (2) या उससे बड़ा और (5) से छोटा है(x) is (2) or more and less than (5)
\(2\le x<5\) में (2) शामिल है पर (5) शामिल नहीं है। संयुक्त असमानता को दो भागों में पढ़ें। / In \(2\le x<5\), (2) is included but (5) is not. Read a compound inequality in two parts.
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Which value is not included in \(0\le x\le 6\)?
D. (7)
(7) संख्या (6) से बड़ी है इसलिए शामिल नहीं है। \(\le\) में केवल सीमा तक के मान आते हैं। / The number (7) is greater than (6), so it is not included. The sign \(\le\) includes values only up to the boundary.
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If \(D_1={x:x\in \mathbb{Z},,2<x^2\leq16}\), what is the roster form of \(D_1\)?
A. \(D_1={-4,-3,-2,2,3,4}\)
\(x^2\leq16\) से \(-4\leq x\leq4\) मिलता है। / \(x^2\leq16\) gives \(-4\leq x\leq4\).
\(2<x^2\) होने से \(x^2\) के मान (4,9,16) ही चलेंगे, इसलिए \(x=\pm2,\pm3,\pm4\)। / Since \(2<x^2\), only square values (4,9,16) work, so \(x=\pm2,\pm3,\pm4\).
संयुक्त असमानता में दोनों भागों को साथ लागू करें। / Apply both parts of a compound inequality together.
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