NCERT Class XI Mathematics - Linear Inequalities - Solutions
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Question : 61
Total: 65
5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47
Solution:
(i) 5(2x – 7) – 3(2x + 3) ≤ 0
⇒ 10x – 35 – 6x – 9 ≤ 0 ⇒ 4x – 44 ≤ 0 ⇒ 4x ≤ 44 ⇒ x ≤ 11
(ii) 2x + 19 ≤ 6x + 47
⇒ 2x – 6x ≤ 47 – 19 ⇒ – 4x ≤ 28
Dividing both sides by – 4, we get x ≥ –7
From (i) and (ii), the solution is –7 ≤ x ≤ 11
i.e., x ∈ [–7, 11]
⇒ 10x – 35 – 6x – 9 ≤ 0 ⇒ 4x – 44 ≤ 0 ⇒ 4x ≤ 44 ⇒ x ≤ 11
(ii) 2x + 19 ≤ 6x + 47
⇒ 2x – 6x ≤ 47 – 19 ⇒ – 4x ≤ 28
Dividing both sides by – 4, we get x ≥ –7
From (i) and (ii), the solution is –7 ≤ x ≤ 11
i.e., x ∈ [–7, 11]
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