Question

Find the values of $x$, which satisfy the inequation $-2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2,x\in W$.

Answer 1

Given: $-2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2$
$\Rightarrow -\frac{17}{6}<\frac{3-4x}{6}\le 2$
Multiplying throughout by $6$
$\Rightarrow -17<3-4x\le 12$
$-17<3-4x$ and $3-4x\le 12$
$\Rightarrow 4x<3+17\Rightarrow 3-12\le 4x$
$\Rightarrow 4x<20\Rightarrow -9\le 4x$
$\Rightarrow x<5\Rightarrow -\frac{9}{4}<x$
$\{5>x\ge \frac{-9}{4}\}$
Hence, the solution set is $\{x:x\in W,-\frac{9}{4}\le x<5\}$

Since $x$ is a whole number,
$\therefore$ Values of $x$ are $\{0,1,2,3,4\}$