Question

Solve the inequalities and represent the solution graphically on number line:
5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47

Answer 1

5(2x – 7) – 3(2x + 3) ≤ 0 ⇒ 10x – 35 – 6x – 9 ≤ 0 ⇒ 4x – 44 ≤ 0 ⇒ 4x ≤ 44
⇒ x ≤ 11 ………………………………… (1)
2x + 19 ≤ 6x + 47 ⇒ 19 – 47 ≤ 6x – 2x ⇒ –28 ≤ 4x
⇒ –7 ≤ x ……………………………… (2)

From (1) and (2), it can be concluded that the solution set for the given system of inequalities is [–7, 11]. The solution of the given system of inequalities can be represented on number line as