The equivalent expressions are:
[tex]5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x +5(7) - \frac{3}{2}x +3(4)[/tex]
[tex]5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{x}{6} + 47[/tex]
[tex]5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{1}{6}x + 35 + 12[/tex]
Solution:
Given expression is:
[tex]5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4)[/tex]
We have to find the equivalent expression
By distributive property,
a(b + c) = ab + ac
Therefore, one of equivalent expression is:
[tex]5(\frac{1}{3}x + 7) - 3(\frac{1}{2}x - 4) = \frac{5}{3}x +5(7) - \frac{3}{2}x +3(4)[/tex]
The other equivalent expressions are:
[tex]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[/tex]
Thus equivalent expression is found
