Mathematics

Solve :
13x - 5 < 15x + 4 < 7x + 12, x ∈ R. Represent the solution set on a real number line.

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Given,

Inequation : 13x - 5 < 15x + 4 < 7x + 12

Solving L.H.S. of the inequation,

⇒ 13x - 5 < 15x + 4

⇒ 15x - 13x > -5 - 4

⇒ 2x > -9

⇒ x > $-\dfrac{9}{2}$ …………(1)

Solving R.H.S. of the inequation,

⇒ 15x + 4 < 7x + 12

⇒ 15x - 7x < 12 - 4

⇒ 8x < 8

⇒ x < $\dfrac{8}{8}$

⇒ x < 1 ………….(2)

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

Solution set = {x ∈ R : $-\dfrac{9}{2}$ < x < 1}.

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