linear inequality se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
107 questions tagged with linear inequality.
Which is the solution set of \(7x+2\geq 3x-18\)?
D. \({x:x\geq -5}\)
\(4x\geq -20\) से \(x\geq -5\) मिलता है। समुच्चय रूप में सही असमानता चिन्ह लिखना जरूरी है। / From \(4x\geq -20\), we get \(x\geq -5\). In set form, writing the correct inequality sign is important.
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If (x) is an integer and (4x-3<21), what is the greatest possible (x)?
B. (5)
(4x<24) से (x<6) मिलता है। (6) से छोटा सबसे बड़ा पूर्णांक (5) है। / From (4x<24), we get (x<6). The greatest integer less than (6) is (5).
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Solve the inequality (5(2x+1)-3x<26).
B. (x<3)
(10x+5-3x<26) से (7x<21) मिलता है। अतः (x<3) सही है। / From (10x+5-3x<26), we get (7x<21). Hence (x<3) is correct.
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Which is the correct solution of (3(x-4)+5\leq 2x+1)?
A. \(x\leq 8\)
सरल करने पर \(3x-7\leq 2x+1\) मिलता है। इसलिए \(x\leq 8\) है। / Simplifying gives \(3x-7\leq 2x+1\). Therefore \(x\leq 8\).
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Solve the inequality \(13-3x\leq 4\).
B. \(x\geq 3\)
\(-3x\leq -9\) में ऋणात्मक संख्या से भाग देने पर चिन्ह बदलता है। इसलिए \(x\geq 3\) सही है। / In \(-3x\leq -9\), dividing by a negative number reverses the sign. Hence \(x\geq 3\) is correct.
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Which is the solution of (2(x-5)+3\geq 3(x-4)-7)?
A. \(x\leq 12\)
सरल करने पर \(2x-7\geq 3x-19\) मिलता है। इससे \(12\geq x\) अर्थात \(x\leq 12\) है। / Simplifying gives \(2x-7\geq 3x-19\). This gives \(12\geq x\), that is \(x\leq 12\).
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A. \(x\geq 4\)
कथन \(2x-9\geq -1\) देता है। इससे \(2x\geq 8\) और \(x\geq 4\) मिलता है। / The statement gives \(2x-9\geq -1\). This gives \(2x\geq 8\) and \(x\geq 4\).
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What is the correct solution of (9-4(x+2)>x-14)?
A. (x<3)
सरल करने पर (1-4x>x-14) मिलता है। इसलिए (15>5x) और (x<3) है। / Simplifying gives (1-4x>x-14). Thus (15>5x) and (x<3).
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For \(7x-4\geq 3x+20\) and integer (x), what is the least possible (x)?
A. (6)
\(4x\geq 24\) से \(x\geq 6\) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (6) है। / From \(4x\geq 24\), we get \(x\geq 6\). Hence the least integer solution is (6).
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Solve the inequality (4-(x-3)\geq 2x+1).
A. \(x\leq 2\)
\(4-x+3\geq 2x+1\) से \(7-x\geq 2x+1\) मिलता है। इसलिए \(6\geq 3x\) और \(x\leq 2\) है। / From \(4-x+3\geq 2x+1\), we get \(7-x\geq 2x+1\). Thus \(6\geq 3x\) and \(x\leq 2\).
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What is the solution of (2(x+1)-3(x-2)<10)?
A. (x>-2)
सरल करने पर (2x+2-3x+6<10) यानी (-x+8<10) मिलता है। इसलिए (-x<2) और (x>-2) है। / Simplifying gives (2x+2-3x+6<10), that is (-x+8<10). So (-x<2) and (x>-2).
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A. (5)
शर्त \(50-8x\geq 10\) है जिससे \(x\leq 5\) मिलता है। अधिकतम पूर्ण संख्या (5) है। / The condition is \(50-8x\geq 10\), giving \(x\leq 5\). The maximum whole number is (5).
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If three times a number decreased by (5) is at least (16), what is the solution?
A. \(x\geq 7\)
कथन \(3x-5\geq 16\) देता है। इससे \(3x\geq 21\) और \(x\geq 7\) मिलता है। / The statement gives \(3x-5\geq 16\). This gives \(3x\geq 21\) and \(x\geq 7\).
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Four times a number is less than (28). What is the correct inequality form?
A. (4x<28)
किसी संख्या को (x) मानें तो उसका (4) गुना (4x) है। कम है का चिन्ह (<) होता है। / Let the number be (x), so four times it is (4x). The phrase less than uses the sign (<).
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What is the correct conclusion for (4x+9<4x+2)?
A. कोई हल नहींNo solution
दोनों तरफ से (4x) घटाने पर (9<2) मिलता है जो असत्य है। अतः कोई हल नहीं है। / Subtracting (4x) from both sides gives (9<2), which is false. Hence there is no solution.
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Why is (x=4) included in the solution of \(2x-3\leq x+1\)?
A. क्योंकि \(x\leq 4\)Because \(x\leq 4\)
हल \(x\leq 4\) है इसलिए (x=4) शामिल है। \(\leq\) में बराबरी भी मान्य होती है। / The solution is \(x\leq 4\), so (x=4) is included. In \(\leq\), equality is also valid.
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Which value satisfies the inequality (4x-6>10)?
A. (x=5)
असमानता से (4x>16) और (x>4) मिलता है। दिए गए विकल्पों में केवल (5) इस शर्त को मानता है। / The inequality gives (4x>16) and (x>4). Among the options, only (5) satisfies this condition.
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Write the solution of \(2x+7\geq 19\) in interval form.
A. \([6,\infty\))
\(2x\geq 12\) से \(x\geq 6\) मिलता है। बराबरी होने पर (6) को बंद कोष्ठक से लिखते हैं। / From \(2x\geq 12\), we get \(x\geq 6\). Since equality is included, write (6) with a closed bracket.
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Which statement is correct after simplifying \(15\leq 4x-1\)?
A. \(x\geq 4\)
\(16\leq 4x\) से \(4\leq x\) अर्थात \(x\geq 4\) मिलता है। बाईं तरफ से पढ़ते समय क्रम को ठीक रखें। / From \(16\leq 4x\), we get \(4\leq x\), that is \(x\geq 4\). Keep the order correct when reading from the left.
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Find the solution of \(\frac{x-1}{3}+\frac{x+2}{2}\leq 4\).
A. \(x\leq \frac{16}{5}\)
(6) से गुणा करने पर \(2x-2+3x+6\leq 24\) मिलता है। इसलिए \(5x\leq 16\) और \(x\leq \frac{16}{5}\) है। / Multiplying by (6) gives \(2x-2+3x+6\leq 24\). So \(5x\leq 16\) and \(x\leq \frac{16}{5}\).
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What is the solution of (2(3x+4)>4x+18)?
A. (x>5)
(6x+8>4x+18) से (2x>10) और (x>5) मिलता है। सख्त असमानता में बराबरी नहीं आती। / From (6x+8>4x+18), we get (2x>10) and (x>5). A strict inequality does not include equality.
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For which (x) is (5(2x-1)\leq 3x+16) true?
A. \(x\leq 3\)
\(10x-5\leq 3x+16\) से \(7x\leq 21\) और \(x\leq 3\) मिलता है। विस्तार के बाद सरल करें। / From \(10x-5\leq 3x+16\), we get \(7x\leq 21\) and \(x\leq 3\). Expand and then simplify.
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What is the solution of (11-4x>3)?
A. (x<2)
(-4x>-8) में (-4) से भाग देने पर (x<2) मिलता है। खुले चिन्ह का अर्थ सीमा शामिल नहीं है। / In (-4x>-8), dividing by (-4) gives (x<2). The strict sign means the boundary is not included.
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Choose the correct solution of (8x-3<5x+12).
A. (x<5)
(3x<15) से (x<5) मिलता है। सीमा बिंदु (5) शामिल नहीं है। / From (3x<15), we get (x<5). The boundary point (5) is not included.
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What do we get after solving \(6-5x\leq 16\)?
A. \(x\geq -2\)
\(-5x\leq 10\) में (-5) से भाग देने पर \(x\geq -2\) होता है। ऋणात्मक भाग से चिन्ह पलटता है। / In \(-5x\leq 10\), dividing by (-5) gives \(x\geq -2\). Division by a negative number reverses the sign.
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Which is the solution set of \(4x+3\geq 2x-5\)?
A. \({x:x\geq -4}\)
\(2x\geq -8\) इसलिए \(x\geq -4\) है। समुच्चय रूप में चर की शर्त साफ लिखें। / Since \(2x\geq -8\), \(x\geq -4\). In set form, write the condition on the variable clearly.
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If (x) is a natural number and \(3x-2\leq 13\), how many values of (x) are possible?
A. (5)
\(3x\leq 15\) से \(x\leq 5\) मिलता है। प्राकृतिक मान (1,2,3,4,5) हैं। / From \(3x\leq 15\), we get \(x\leq 5\). The natural values are (1,2,3,4,5).
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Which inequality includes (x=4) in its solution but does not include (x=3)?
B. \(2x-5\geq 3\)
\(2x-5\geq 3\) से \(x\geq 4\) मिलता है इसलिए (4) शामिल है और (3) नहीं। सीमा वाले विकल्प में बराबरी जरूर जांचें। / \(2x-5\geq 3\) gives \(x\geq 4\), so (4) is included and (3) is not. Always check equality at boundary options.
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Which option is the solution of \(6-4x\geq 2x-12\)?
A. \(x\leq 3\)
\(18\geq 6x\) से \(x\leq 3\) मिलता है। पक्ष बदलते समय असमानता की दिशा को सावधानी से पढ़ें। / \(18\geq 6x\) gives \(x\leq 3\). Read the direction carefully when rearranging sides.
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If (2a-3<7), what is the correct bound for (a)?
A. (a<5)
(2a<10) से (a<5) मिलता है। धनात्मक गुणांक से भाग देने पर चिन्ह नहीं बदलता।
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