Question

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

`- 8 1/2 < - 1/2 - 4x ≤ 7 1/2, x ∈ I`

Answer 1

Given,

⇒ `- 8 1/2 < - 1/2 - 4x ≤ 7 1/2`

⇒ `- 17/2 < - 1/2 - 4x ≤ 15/2`

Solving L.H.S. of the inequation,

⇒ `- 17/2 < - 1/2 - 4x`

⇒ `4x < 17/2 - 1/2`

⇒ `4x < 16/2`

⇒ 4x < 8

⇒ `x < 8/4`

⇒ x < 2   ...(1)

Solving R.H.S. of the inequation,

⇒ `-1/2 - 4x ≤ 15/2`

⇒ `- 4x ≤ 15/2 + 1/2`

⇒ `- 4x ≤ 16/2`

⇒ – 4x ≤ 8

Dividing by –4 on both sides we get,

⇒ x ≥ –2   ...(As on dividing by negative number the sign reverses)

⇒ x ≥ –2   ...(2)

From (1) and (2) we get,

–2 ≤ x < 2

Since, x ∈ I

Hence, solution set = {–2, –1, 0, 1}.

Solution on the number line is: