Question

Solve and graph the solution set of:

x + 5 ≥ 4(x – 1) and 3 – 2x < –7, x ∈ R

Answer 1

Given: x + 5 ≥ 4(x – 1) and 3 – 2x < –7

⇒ x + 5 ≥ 4x – 4

4x – x ≤ 5 + 4

3x ≤ 9

Dividing both sides by 3 we get,

x ≤ 3     ...(i)

3 – 2x < –7

2x > 3 + 7

2x > 10

x > 5     ...(ii)   

From (i) and (ii) we get,

x ≤ 3 and x > 5