Solve 3/4(x-8)leq8

$$3 / 4 ( x - 8 ) \leq 8$$

Solve for x

$$x\leq \frac{56}{3}$$

Solution Steps

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}. Since \frac{3}{4} is positive, the inequality direction remains the same.

$$x-8\leq 8\times \frac{4}{3}$$

Express 8\times \frac{4}{3} as a single fraction.

$$x-8\leq \frac{8\times 4}{3}$$

Multiply 8 and 4 to get 32.

$$x-8\leq \frac{32}{3}$$

Add 8 to both sides.

$$x\leq \frac{32}{3}+8$$

Convert 8 to fraction \frac{24}{3}.

$$x\leq \frac{32}{3}+\frac{24}{3}$$

Since \frac{32}{3} and \frac{24}{3} have the same denominator, add them by adding their numerators.

$$x\leq \frac{32+24}{3}$$

Add 32 and 24 to get 56.

$$x\leq \frac{56}{3}$$