Question

Find the values of x, which satisfy the inequation

${\displaystyle -2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2}$, x ∈ W

Graph the solution set on the number line.

Answer 1

We need to find the values of x, such that x satisfies the inequation ${\displaystyle -2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2\in W}$

Consider the given inequation:

${\displaystyle -2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2,x \in W}$

Consider the given inequation

${\displaystyle -2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3} \le 2}$

${\displaystyle \Rightarrow \frac{-17}{6}<\frac{3-4x}{6}\le \frac{12}{6}}$

${\displaystyle \Rightarrow \frac{17}{6} >\frac{4x-3}{6}\ge \frac{-12}{6}}$

${\displaystyle \Rightarrow 17>4x-3<17}$

${\displaystyle \Rightarrow -12+3\le 4x -3+3<17+3}$

${\displaystyle \Rightarrow -9\le 4x<20}$

${\displaystyle \Rightarrow -\frac{9}{4}\le \frac{4x}{4}<\frac{20}{4}}$

${\displaystyle \Rightarrow -\frac{9}{4}\le x<5}$

Since x ∈ W, the values of x are 0, 1, 2. 3, 4

And the required line is