Question

Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options.

Answer 1

The equivalent expressions are:

$5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x +5(7) - \frac{3}{2}x +3(4)$

$5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{x}{6} + 47$

$5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{1}{6}x + 35 + 12$

Solution:

Given expression is:

$5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4)$

We have to find the equivalent expression

By distributive property,

a(b + c) = ab + ac

Therefore, one of equivalent expression is:

$5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x +5(7) - \frac{3}{2}x +3(4)$

The other equivalent expressions are:

$5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x + 35 - \frac{3}{2}x +12\\\\Combine\ the\ like\ terms\\\\5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{10-9}{6}x + 35 + 12\\\\Simplify\ the\ above\\\\5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{1}{6}x + 35 + 12\\\\5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{x}{6} + 47$

Thus equivalent expression is found