Mathematics

Solve the following inequation, write down the solution set and represent it on the real number line. -2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ R.

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Inequation : -2 + 10x ≤ 13x + 10 < 24 + 10x

Solving L.H.S. of the above inequation,

⇒ -2 + 10x ≤ 13x + 10

⇒ 13x - 10x ≥ -2 - 10

⇒ 3x ≥ -12

⇒ x ≥ $-\dfrac{12}{3}$

⇒ x ≥ -4 ………..(1)

Solving R.H.S. of the above inequation,

⇒ 13x + 10 < 24 + 10x

⇒ 13x - 10x < 24 - 10

⇒ 3x < 14

⇒ x < $\dfrac{14}{3}$

⇒ x < $4\dfrac{2}{3}$ ………..(2)

From equation (1) and (2), we get :

⇒ -4 ≤ x $\lt 4\dfrac{2}{3}$

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