Question

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

2x – 5 ≤ 5x + 4 < 11, x ∈ R

Answer 1

Given,

⇒ 2x – 5 ≤ 5x + 4 < 11

Solving L.H.S. of the inequation,

⇒ 2x – 5 ≤ 5x + 4

⇒ 5x + 4 ≥ 2x – 5

⇒ 5x – 2x ≥ –5 – 4

⇒ 3x ≥ –9

⇒ `x ≥ - 9/3`

⇒ x ≥ –3   ...(1)

Solving R.H.S. of the inequation,

⇒ 5x + 4 < 11

⇒ 5x < 11 – 4

⇒ 5x < 7

⇒ `x < 7/5`

⇒ x < 1.4   ...(2)

From (1) and (2) we get,

–3 ≤ x < 1.4

Since, x ∈ R

Hence, solution set = {x : –3 ≤ x < 1.4, x ∈ R}.

Solution on the number line is :