Question

Solve, −3 ≤ −3x + 2 < 4, x ∈ R.

Answer 1

We have, 

−3 ≤ −3x + 2 <4,

⇒ −3 − 2 ≤ −3x + 2 − 2 < 4 − 2

(Adding -2 in inequality)

⇒ −5 ≤ −3x < 2

⇒ \(\frac{-5}{-3}\) ≥ \(\frac{-3x}{-3}\) >\(\frac{2}{-3}\)  (Dividing by −3)

Or ⇒ \(-\frac{2}{3}\) > x ≤ \(-\frac{5}{3}\)

Or x ∈\(-\frac{2}{3}\),\(-\frac{5}{3}\)