Mathematics

Solve the inequation given below. Write the solution set and represent it on the number line:
–1 ≤ 3 + 4x < 23, x ∈ R

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Solving L.H.S. of the inequation,

⇒ –1 ≤ 3 + 4x

⇒ 3 + 4x ≥ -1

⇒ 4x ≥ -1 - 3

⇒ 4x ≥ -4

⇒ x ≥ $-\dfrac{4}{4}$

⇒ x ≥ -1 …..(1)

Solving R.H.S. of the inequation,

⇒ 3 + 4x < 23

⇒ 4x < 23 - 3

⇒ 4x < 20

⇒ x < $\dfrac{20}{4}$

⇒ x < 5 ………(2)

From (1) and (2) we get,

-1 ≤ x < 5

Since, x ∈ R

Hence, solution set = {x : -1 ≤ x < 5, x ∈ R}.

Solution on the number line is :

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