Question

Which expression is equivalent to

Answer 1

Answer:

Given expression $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$ is equivalent to the expression $2(4x-3)$.

Step-by-step explanation:

Given expression is  $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$

To simplify the expression:

$\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})=\frac{18x-12}{3}+\frac{4x-4}{2}$

Taking LCM 6 to the above expression we get

$=\frac{(18x-12)2+3(4x-4)}{6}$ (Applying multiplication rules)

$=\frac{36x-24+12x-12}{6}$  ( doing sums to the terms)

$=\frac{48x-36}{6}$

$=8x-6$

We can take common number 2 outside to the above expression

$=2(4x-3)$

Therefore  $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})=2(4x-3)$

Therefore given expression $\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})$ is equivalent to the expression $2(4x-3)$.