Answer
$$z=-2$$
Work Step by Step
$$\frac{3}{4}(24 - 8z) - 16 = -\frac{2}{3}(6z - 9)$$
Simplify the left side of the equation by distributing $\frac{3}{4}$ to the terms inside the parentheses:
$$\frac{3}{4}(24 - 8z) - 16$$
$$=[24(\frac{3}{4}) - 8z(\frac{3}{4})] - 16$$ $$=18-6z - 16$$ $$= 2-6z$$
Simplify the right side of the equation by distributing $-\frac{2}{3}$ to the terms inside the parentheses: $$-\frac{2}{3}(6z - 9)$$ $$=[6z(-\frac{2}{3})-9(-\frac{2}{3})]$$ $$= -4z + 6$$
Rewrite the equation using the simplified forms:
$$2-6z = -4z + 6$$ Subtract $2$ from both sides: $$2-2-6z = -4z + 6 - 2$$ $$-6z= -4x + 4$$ Simplify: $$-2z = 4$$ Divide both sides by $-2$: $$z = -2$$
Check:
$$\frac{3}{4}(24 - 8(-2)) - 16 = -\frac{2}{3}(6(-2) - 9)$$ $$\frac{3}{4}(24 + 16) - 16 = -\frac{2}{3}(-12 - 9)$$ $$\frac{3}{4}(40) - 16 = -\frac{2}{3}(-21)$$ $$30 - 16 = -(-14)$$ $$14 = 14 --> TRUE$$
