Question

Solve the inequation given below. Write the solution set and represent it on the number line:

2 + 4x < 2x – 5 < 3x, x ∈ I

Answer 1

Given,

⇒ 2 + 4x < 2x – 5 < 3x

Solving L.H.S. of the inequation,

⇒ 2 + 4x < 2x – 5

⇒ 4x – 2x < –5 – 2

⇒ 2x < –7

⇒ `x < -7/2`

⇒ x < –3.5   ...(1)

Solving R.H.S. of the inequation,

⇒ 2x – 5 < 3x

⇒ 3x – 2x > –5

⇒ x > –5   ...(2)

From (1) and (2) we get,

–5 < x < –3.5

Since, x ∈ I.

Hence, solution set = {–4}.

Solution on the number line is: