Question

Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.

Answer 1

2x – 5 ≤ 5x + 4 < 11 2x – 5 ≤ 5x + 4
⇒ 2x – 5 – 4 ≤ 5x and 5x + 4 < 11
⇒ 2x – 9 ≤ 5x and 5x < 11 – 4
and 5x < 7
⇒ 2x – 5x ≤ 9 and x < `(7)/(5)`
⇒ 3x > – 9 and x< 1.4
⇒ x > – 3