Question

Find the vlaues of x, which satisfy the inequation
$-2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2,xϵW$ Graph the solution set on the number line.
[3 MARKS]

Answer 1

Solving each inequation: 1 Mark each
Solution on the graph: 1 Mark

Given $-2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2,xϵW\Rightarrow -2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}and\frac{1}{2}-\frac{2x}{3}\le 2\Rightarrow -\frac{17}{6}<\frac{1}{2}-\frac{2x}{3}and\frac{1}{2}-2\le \frac{2x}{3}\Rightarrow \frac{2x}{3}<\frac{1}{2}+\frac{17}{6}and-\frac{3}{2}\le \frac{2x}{3}\Rightarrow \frac{2x}{3}<\frac{20}{6}and-\frac{9}{4}\le x\Rightarrow x<5and-2\frac{1}{4}\le x\Rightarrow -2\frac{1}{4}\le x<5,xϵWSolutionset\Rightarrow \{0,1,2,3,4\}$
The graph of the solution set is shown by thick dots.