Question

Solve and show the given inequality on the number line : 

– 5 ≤ 3x – 2 < 7, where x ∈ R

Answer 1

The given inequality can be split into two inequalities : 

–5 ≤ 3x – 2 and 3x – 2 < 7 

⇒ –5 + 2 ≤ 3x and 3x < 7 + 2 ⇒ –3 ≤ 3x and 3x < 9 

⇒ -1 ≤ x and x < 3 ⇒ -1 ≤ x < 3 

This can be shown on a number line as :