Question

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

–3 < 2x – 1 < x + 4, x ∈ I

Answer 1

Given,

⇒ –3 < 2x – 1 < x + 4

Solving L.H.S. of the inequation,

⇒ –3 < 2x – 1

⇒ 2x – 1 > –3

⇒ 2x > –3 + 1

⇒ 2x > –2

⇒ `x > (-2)/2`

⇒ x > –1   ...(1)

Solving R.H.S. of the inequation,

⇒ 2x – 1 < x + 4

⇒ 2x – x < 4 + 1

⇒ x < 5   ...(2)

From (1) and (2) we get,

⇒ –1 < x < 5

Since, x ∈ I.

Hence, solution set = {0, 1, 2, 3, 4}.

Solution on the number line is: