Question

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

`-2 ≤ 1/2 - (2x)/3 < 1 5/6, x ∈ I`

Answer 1

Solving L.H.S. of the inequation,

⇒ `-2 ≤ 1/2 - (2x)/3`

⇒ `1/2 - (2x)/3 ≥ -2`

⇒ `- (2x)/3 ≥ -2 - 1/2`

⇒ `- (2x)/3 ≥ - 5/2`

Multiplying by –6 on both sides we get,

⇒ 4x ≤ 15   ...(As on multiplying by negative number the sign reverses)

⇒ `x ≤ 15/4`

⇒ x ≤ 3.75   ...(1)

Solving R.H.S. of the inequation,

⇒ `1/2 - (2x)/3 < 1 5/6`

⇒ `1/2 - (2x)/3 < 11/6`

⇒ `- (2x)/3 < 11/6 - 1/2`

⇒ `- (2x)/3 < (11 - 3)/6`

⇒ `- (2x)/3 < 8/6`

⇒ `- 2x < 8/6 xx 3`

⇒ –2x < 4

Dividing both sides by –2, we get:

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

From (1) and (2) we get,

–2 > x ≤ 3.75

Since, x ∈ I

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

Solution on the number line is :