Question

Solve the following inequalities and represent the solution graphically on number line: 

3x – 7 > 2(x – 6),

 6 – x > 11 – 2x

Answer 1

3x – 7 > 2(x – 6) ⇒ 3x – 7 > 2x – 12 ⇒ 3x – 2x > – 12 + 7
⇒ x > –5 …………………….… (1)
6 – x > 11 – 2x ⇒ –x + 2x > 11 – 6
⇒ x > 5 ………………………… (2)

From (1) and (2), it can be concluded that the solution set for the given system of inequalities is (5, ∞). The solution of the given system of inequalities can be represented on number line as