Question

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

–2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ Z

Answer 1

Given,

⇒ –2 + 10x ≤ 13x + 10 < 24 + 10x

Solving L.H.S. of the inequation,

⇒ –2 + 10x ≤ 13x + 10

⇒ 13x + 10 ≥ –2 + 10x

⇒ 13x – 10x ≥ –2 – 10

⇒ 3x ≥ –12

⇒ `x ≥ - 12/3`

⇒ x ≥ –4   ...(1)

Solving R.H.S. of the inequation,

⇒ 13x + 10 < 24 + 10x

⇒ 13x – 10x < 24 – 10

⇒ 3x < 14

⇒ `x < 14/3`

⇒ x < 4.6   ...(2)

From (1) and (2) we get,

⇒ –4 ≤ x < 4.6

Since, x ∈ Z

Hence, solution set = {–4, –3, –2, –1, 0, 1, 2, 3, 4}.

Solution on the number line is: