NCERT Class XI Mathematics - Linear Inequalities - Solutions
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Question : 14
Total: 65
37 – (3x + 5) ≥ 9x – 8(x – 3)
Solution:
The inequality is 37 – (3x + 5) ≥ 9x – 8(x – 3)
Simplifying, 37 – 3x – 5 ≥ 9x – 8x + 24 or 32 – 3x ≥ x + 24
Transposing x to L.H.S. and 32 to R.H.S., We get –3x – x ≥ 24 – 32 or – 4x ≥ – 8
Dividing both sides by – 4, we get x ≤ 2
∴ The solution is (– ∞, 2].
Simplifying, 37 – 3x – 5 ≥ 9x – 8x + 24 or 32 – 3x ≥ x + 24
Transposing x to L.H.S. and 32 to R.H.S., We get –3x – x ≥ 24 – 32 or – 4x ≥ – 8
Dividing both sides by – 4, we get x ≤ 2
∴ The solution is (– ∞, 2].
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