Question

Solve the inequalities for real x for the following equation: $\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}$.

Answer 1

$\dfrac{3(x-2)}{5} \leq \dfrac{5(2-x)}{3}$

Multiply both sides by 5 and 3:

$9(x - 2) \leq 25(2 - x)$

Distribute 9 and 25:

$9x - 18 \leq 50 - 25x$

Add 25x and 18 to both sides:

$9x+ 25x \leq 50 +18$

Combine like terms:

$34x \leq 68$

Divide both sides by 34:

$x \leq 2$