Question

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

`-2 2/3 ≤ x + 1/3 < 3 1/3, x ∈ R`

Answer 1

⇒ `-2 2/3 ≤ x + 1/3 < 3 1/3`

⇒ `-8/3 ≤ x + 1/3 < 10/3`

Solving L.H.S. of the inequation,

⇒ `-8/3 ≤ x + 1/3`

⇒ `x + 1/3 ≥ -8/3`

⇒ `x ≥ -8/3 - 1/3`

⇒ `x ≥ -9/3`

⇒ x ≥ –3   ...(1)

Solving R.H.S. of the inequation,

⇒ `x + 1/3 < 10/3`

⇒ `x < 10/3 - 1/3`

⇒ `x < 9/3`

⇒ x < 3   ...(2)

From (1) and (2) we get,

–3 ≤ x < 3

Since, x ∈ R

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

Solution on the number line is: