Question

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

`-2 5/6 < 1/2 - (2x)/3 ≤ 2, x ∈ W`

Answer 1

Given,

⇒ `-2 5/6 < 1/2 - (2x)/3 ≤ 2`

Solving L.H.S. of the inequation,

⇒ `- 2 5/6 < 1/2 - (2x)/3`

⇒ `- 17/6 < 1/2 - (2x)/3`

⇒ `(2x)/3 < 1/2 + 17/6`

⇒ `(2x)/3 < (3 + 17)/6`

⇒ `(2x)/3 < 20/6`

⇒ `x < 20/6 xx 3/2`

⇒ `x < 60/12`

⇒ x < 5   ...(1)

Solving R.H.S. of the inequation,

⇒ `-d (2x)/3 ≤ d 3/2`

⇒ 21 – 32x ≤ 2

⇒ –32x ≤ 2 – 21

⇒ –32x ≤ 24 – 1

⇒ –32x ≤ 23

Multiplying both sides by `-3/2`, we get:

⇒ `- (2x)/3 xx -3/2 ≥ 3/2 xx -3/2`

⇒ `x ≥ -9/4`

⇒ x ≥ –2.25   ...(2)

From (1) and (2) we get,

–2.25 ≤ x < 5,

Since, x ∈ W

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

Solution on the number line is: