Question

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

–1 ≤ 3 + 4x < 23, x ∈ R

Answer 1

Solving L.H.S. of the inequation,

⇒ –1 ≤ 3 + 4x

⇒ 3 + 4x ≥ –1

⇒ 4x ≥ –1 – 3

⇒ 4x ≥ –4

⇒ `x ≥ - 4/4`

⇒ x ≥ –1   ...(1)

Solving R.H.S. of the inequation,

⇒ 3 + 4x < 23

⇒ 4x < 23 – 3

⇒ 4x < 20

⇒ `x < 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: