Question

which expression is equivalent to $(6x^{2}-9x - 24)\frac{2}{3}$?
a) $6x^{2}-6x - 16$
b) $6x^{2}-9x - 16$
c) $4x^{2}+6x - 16$
d) $4x^{2}-6x - 16$

Explanation:

Step1: Distribute the division

We divide each term in $6x^{2}-9x - 24$ by $\frac{3}{2}$.
Dividing $6x^{2}$ by $\frac{3}{2}$ gives $6x^{2}\div\frac{3}{2}=6x^{2}\times\frac{2}{3}=4x^{2}$.
Dividing $-9x$ by $\frac{3}{2}$ gives $-9x\div\frac{3}{2}=-9x\times\frac{2}{3}=-6x$.
Dividing $-24$ by $\frac{3}{2}$ gives $-24\div\frac{3}{2}=-24\times\frac{2}{3}=-16$.

Step2: Combine the results

The equivalent expression is $4x^{2}-6x - 16$.

Answer:

D. $4x^{2}-6x - 16$