Question

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

`-2/3 < 1 + x/3 ≤ 2/3, x ∈ R`

Answer 1

Solving L.H.S. of the inequation,

⇒ `-2/3 < 1 + x/3`

⇒ `1 + x/3 > - 2/3`

⇒ `x/3 > - 2/3 - 1`

⇒ `x/3 > (-2 - 3)/3`

⇒ `x/3 > (-5)/3`

⇒ `x > (-5)/3 xx 3`

⇒ x > –5   ...(1)

Solving R.H.S. of the inequation,

⇒ `1 + x/3 ≤ 2/3`

⇒ `(3 + x)/3 ≤ 2/3`

⇒ x + 3 ≤ 2

⇒ x ≤ 2 – 3

⇒ x ≤ –1   ...(2)

From (1) and (2) we get,

–5 < x ≤ –1

Since, x ∈ R

Hence, solution set = {x : –5 < x ≤ –1, x ∈ R}.

Solution on the number line is: