Solve and graph the solution set of :

x + 5 ≥ 4(x - 1) and 3 - 2x < -7; x ∈ R.

Given,

x + 5 ≥ 4(x - 1) and 3 - 2x < -7

Solving, x + 5 ≥ 4(x - 1)

⇒ x + 5 ≥ 4x - 4

⇒ 4x - x ≤ 5 + 4

⇒ 3x ≤ 9

Dividing both sides by 3 we get,

⇒ x ≤ 3 …….(i)

Solving, 3 - 2x < -7

⇒ 2x > 3 + 7

⇒ 2x > 10

⇒ x > 5 …….(ii)

From (i) and (ii) we get,

x ≤ 3 and x > 5

There is no number possible which is less than or equal to 3 and greater than 5 hence, no solution.

Hence, solution set is an empty set.