Solve the inequality $\frac{2x-3}{4} \le \frac{5-x}{5}$ . Answer ...

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Worked solution

1. Clear the fractions without changing the inequality direction

$\frac{2x-3}{4} \leqslant \frac{5-x}{5}$
Multiply both sides by $20$ :
$5(2x-3) \leqslant 4(5-x)$

2. Expand and isolate $x$

$10x-15 \leqslant 20-4x$
$14x \leqslant 35$
$x \leqslant \frac{35}{14}=\frac{5}{2}$

Answer

$x \leqslant \dfrac{35}{14}$ , or $x \leqslant \dfrac{5}{2}$

AI analysis — may contain mistakes.

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