Question

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

2 ≤ 2x – 3 ≤ 5, x ∈ R

Answer 1

Given,

⇒ 2 ≤ 2x – 3 ≤ 5

Solving L.H.S. of the inequation,

⇒ 2 ≤ 2x – 3

⇒ 2x – 3 ≥ 2

⇒ 2x ≥ 2 + 3

⇒ 2x ≥ 5

⇒ `x ≥ 5/2`

⇒ `x ≥ 2 1/2`   ...(1)

Solving R.H.S. of the inequation,

⇒ 2x – 3 ≤ 5

⇒ 2x ≤ 5 + 3

⇒ 2x ≤ 8

⇒ `x ≤ 8/2`

⇒ x ≤ 4   ...(2)

From (1) and (2) we get,

`2 1/2 ≤ x ≤ 4`

Since, x ∈ R

Hence, solution set = `{x : 2 1/2 ≤ x ≤ 4, x ∈ R}`.

Solution on the number line is: