Question

Solve the following inequation, write down the solution set and represent it on the real number line:

–2 + 10x ≤ 13x + 10 < 24 + 10x, x 𝜖 Z

Answer 1

Given inequation: –2 + 10x ≤ 13x + 10 < 24 + 10x, x 𝜖 Z

⇒ `-2 + 10x <= 13x + 10` and 13x + 10 < 24 + 10x

⇒ `-2 - 10 <= 13x - 10x` and 13x - 10x < 24 - 10

⇒ `-12 <= 3x`  and 3x < 14

⇒ `-4 <= x`  and x < 4.6

∴ Solution set {x : 4 x 4.6 and x ∈ Z)

Representation on number line is as follows: