Question

Find the range of values of x which satisfy $\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$, where x ϵ real number.

• A. 2 ≤ x < 3
• B. 2 < x < 3
• C. 2 ≤ x ≤ 3
• D. None of these

Answer 1

The correct option is A

2 ≤ x < 3

$\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$

$\frac{-1}{3}\le \frac{3x-8}{6}<\frac{1}{6}$ [Multiply with 6 throughout]

$-2\le (3x-8)<1$

$6\le 3x<9$

$2\le x<3$