NCERT Class XI Mathematics - Linear Inequalities - Solutions
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Question : 59
Total: 65
2(x – 1) < x + 5, 3(x + 2) > 2 – x
Solution:
(i) 2(x – 1) < x + 5 or 2x – 2 < x + 5
⇒ 2x – x < 5 + 2 ⇒ x < 7
(ii) 3(x + 2) > 2 – x or 3x + 6 > 2 – x
⇒ 3x + x > 2 – 6
⇒ 4x > –4 ⇒ x > –1
From (i) and (ii), we get
–1 < x < 7
⇒ 2x – x < 5 + 2 ⇒ x < 7
(ii) 3(x + 2) > 2 – x or 3x + 6 > 2 – x
⇒ 3x + x > 2 – 6
⇒ 4x > –4 ⇒ x > –1
From (i) and (ii), we get
–1 < x < 7
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