Question
Solve the following linear in$-$equation and graph the solution set on a real number line: $\frac{1}{3}(5 x-8) \geq \frac{1}{2}(4 x-7), x \in R$
✓
Answer
$\frac{1}{3}(5 x-8) \geq \frac{1}{2}(4 x-7)$
$2(5 x-8) \geq 3(4 x-7)$
$10 x-16 \geq 12 x-21$
$10 x-12 x \geq-21+16$
$-2 x \geq-5$
$x \leq \frac{5}{2}$
$x \leq 2 \frac{1}{2}$
$\text { Solution set }=\left[x \leq 2 \frac{1}{2}\right]$
$2(5 x-8) \geq 3(4 x-7)$
$10 x-16 \geq 12 x-21$
$10 x-12 x \geq-21+16$
$-2 x \geq-5$
$x \leq \frac{5}{2}$
$x \leq 2 \frac{1}{2}$
$\text { Solution set }=\left[x \leq 2 \frac{1}{2}\right]$
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