Question

How do I do this (Comes With Picture) if someone could help me with this that would be amazing :)

Answer 1

The error occurs in step 3. The student did not distribute the negative properly to every term inside the parenthesis. Below is one proper way to solve for y

$3 - \left(y + \frac{1}{2}\right) = 8$

$3-3 - \left(y + \frac{1}{2}\right) = 8-3$

$-\left(y + \frac{1}{2}\right) = 5$ <--- Note the negative and the parenthesis

$-y - \frac{1}{2} = 5$ <--- Note how we have -1/2 and not +1/2

$-y - \frac{1}{2}+\frac{1}{2} = 5+\frac{1}{2}$

$-y = 5\frac{1}{2}$

$y = -5\frac{1}{2}$

So the proper final answer is $y = -5\frac{1}{2}$
(this is a mixed number which converts to the decimal number -5.5)