Question

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

`(-x)/3 ≤ x/2 - 1 1/3 < 1/6, x ∈ R`

Answer 1

Given,

`(-x)/3 ≤ x/2 - 1 1/3 < 1/6`

Solving L.H.S. of the inequation,

⇒ `-x/2 ≤ x/2 - 1 1/3` 

⇒ `-x/3 - x/2 ≤ -4/3`

⇒ `(-2x - 3x)/6 ≤ -4/3`

⇒ `(-5x)/6 ≤ -4/3`

⇒ `(5x)/6 ≥ -4/3`

⇒ `x ≥ 4/3 xx 6/5`

⇒ `x ≥ 8/5`

⇒ x ≥ 1.6   ...(1)

Solving R.H.S. of the inequation,

⇒ `x < d 9/6 xx 2`

⇒ x < 3   ...(2)

⇒ 2x – 131 < 61

⇒ 2x – 34 < 61

⇒ 2x < 61 + 34

⇒ 2x < 61 + 8

⇒ 2x < 69

⇒ x < 69 × 2

⇒ x < 3   ...(2)

From (1) and (2) we get,

⇒ 1.6 ≤ x < 3

Since, x ∈ R

Hence, solution set = {x : 1.6 ≤ x < 3, x ∈ R}.

Solution on the number line is: