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NCERT Class XI Mathematics - Linear Inequalities - Solutions

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Question : 54 of 65
Marks: +1, -0
- 3 ≤ 4 - 7x2\frac{7x}{2} ≤ 18
Solution:  
Subtracting 4, we get - 3 - 4 ≤ 4 - 7x2\frac{7x}{2} - 4 ≤ 18 - 4 or - 7 ≤ 7x2\frac{-7x}{2} ≤ 14
Multiplying each side by − 27\frac{2}{7} , we get
- 7 × (27)\left(-\frac{2}{7}\right)72\frac{-7}{2} x × (17)\left(-\frac{1}{7}\right) ≥ 14 × (27)\left(-\frac{2}{7}\right)
2 ≥ x ≥ – 4 or –4 ≤ x ≤ 2
∴ x is less than or equal to 2 and greater than or equal to –4. i.e., x ∈ [– 4, 2]
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