Question

Solve the following inequation, write the solution set and represent it on the real number line.

`−1< (2x − 3)/3 − x/5 ≤ 1, x ∈ R​`

Answer 1

Given: `−1< (2x − 3)/3 − x/5 ≤ 1, x ∈ R`

Solving L.H.S of the inequation,

⇒ `−1< (2x − 3)/3 − x/5`

⇒ `−1< (10x − 15 − 3x)/15`

⇒ `−1< (7x − 15)/15`

⇒ −15 < 7x − 15

⇒ −15 + 15 < 7x

⇒ 0 < 7x

⇒ x > 0

Solving R.H.S of the inequation,

⇒ `(2x − 3)/3 − x/5 ≤ 1`

⇒ `(10x − 15 − 3x)/3 ≤ 1`

⇒ `(7x − 15)/3 ≤ 1`

⇒ 7x − 15 ≤ 15

⇒ 7x ≤ 15 + 15

⇒ 7x ≤ 30

`⇒ x ≤ 30/7`

∴ `0 < x < 30/7`

Solution set = `(0, 30/7]`