Solve the inequality - 6 ≤ 6-4x/3 ≤ 8

Question

Solve the inequality - 6 ≤ \(\frac{6-4x}{3}\) ≤ 8

Answer 1

- 6 ≤  \(\frac{6-4x}{3}\) ≤ 8

Multiplying (i) by 3

- 6 × 3 ≤ 3 × \(\frac{6-4x}{3}\) ≤ 3 × 8

or - 18 ≤ 6 - 4x ≤ 24

or - 18 - 6 ≤ - 4x ≤ 24 - 6

or - 24 ≤ - 4x ≤ 18

or - 6 ≤ - x ≤ \(\frac{9}{2}\) (Dividing by 4)

or 6 ≥ x ≥ - \(\frac{9}{2}\) [Multiplying by (- 1)]

or - \(\frac{9}{2}\) ≤ x ≤ 6

[Multiplying by (-1), sign ≤ converts into ≥]

Thus, solution region x ∈ [\(-\frac{9}{2}\), 6]

Note: We know that - 2 < - 1, when remove - ve sign then 2 > 1.