Question
Solve the following linear in-equation and graph the solution set on a real number line:
$-3 \leq \frac{1}{2}-\frac{2 x }{3} \leq 2 \frac{2}{3}, x \in N$
$-3 \leq \frac{1}{2}-\frac{2 x }{3} \leq 2 \frac{2}{3}, x \in N$
✓
Answer
$-3 \leq \frac{1}{2}-\frac{2 x }{3}$
$-3 \leq \frac{3-4 x }{6}$
$-18 \leq 3-4 x$
$-18-3 \leq-4 x$
$-21 \leq-4 x$
$x \leq \frac{21}{4}$
$x \leq 5 \frac{1}{4}$
and
$\frac{1}{2}-\frac{2 x}{3} \leq 2 \frac{2}{3}$
$\frac{3-4 x}{6} \leq \frac{8}{3}$
$9-12 x \leq 48$
$-12 x \leq 39$
$12 x \geq-39$
$x \geq-3 \frac{1}{4} $
Solution set $=\left[-3 \frac{1}{4} \leq x \leq 5 \frac{1}{4}\right]$
$-3 \leq \frac{3-4 x }{6}$
$-18 \leq 3-4 x$
$-18-3 \leq-4 x$
$-21 \leq-4 x$
$x \leq \frac{21}{4}$
$x \leq 5 \frac{1}{4}$
and
$\frac{1}{2}-\frac{2 x}{3} \leq 2 \frac{2}{3}$
$\frac{3-4 x}{6} \leq \frac{8}{3}$
$9-12 x \leq 48$
$-12 x \leq 39$
$12 x \geq-39$
$x \geq-3 \frac{1}{4} $
Solution set $=\left[-3 \frac{1}{4} \leq x \leq 5 \frac{1}{4}\right]$
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