Solve the inequality 2 (x – 1) 2 – x and represent the solution graphically on number line.

Question

Solve the inequality 2 (x – 1) < x + 5, 3 (x + 2) > 2 – x and represent the solution graphically on number line.

Philoid · Accepted Answer

Given inequalities 2 (x – 1) < x + 5 and 3 (x + 2) > 2 – x

2 ( x – 1) < x + 5

⇒ 2x – 2 < x + 5

⇒ 2x – x < 5 + 2

⇒ x < 7 ………(I)

3 (x + 2) > 2 – x

⇒ 3x + 6 > 2 – x

⇒ 3x + x > 2 – 6

⇒ 4x > -4

⇒ x > -1 ……….(II)

From (I) and (II) we conclude that solution of given inequalities is (-1, 7).