Question

Find the values of x, which satisfy the relation:
$-2\le \frac{1}{2}-\frac{2x}{3}\le 1\frac{5}{6},x\in N$. Also represent the solution on a number line.

Answer 1

$-2\le \frac{1}{2}-\frac{2x}{3}\le \frac{15}{6}\Rightarrow -2\le \frac{1}{2}-\frac{2x}{3}\le \frac{11}{6}$

Multiply the entire inequation by $6$

$\Rightarrow -12\le 3-4x\le 11$

Add ${}^{\prime }-3^{\prime }$ in the entire inequation

$\Rightarrow -15\le -4x\le 8$

Multiply the entire equation by ${}^{\prime }{1}^{\prime }$ which will result in the reversing of the inequality sign.

$\Rightarrow -8\le 4x\le +15\Rightarrow -2\le x\le \frac{15}{4}\therefore xϵ[-2,\frac{15}{4}]$