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

-2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ Z

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 ≥ $-\dfrac{12}{3}$

⇒ x ≥ -4 …….(1)

Solving R.H.S. of the inequation,

⇒ 13x + 10 < 24 + 10x

⇒ 13x - 10x < 24 - 10

⇒ 3x < 14

⇒ x < $\dfrac{14}{3}$

⇒ 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 :