# How do you solve abs(7-y)=4?

Apr 4, 2018

y = 3 and y = 11

#### Explanation:

Because we are taking the absolute value of $7 - y$, we set up two equations that correspond to the negative and positive outcomes of $| 7 - y |$

$7 - y = 4$
and
$- \left(7 - y\right) = 4$

This is because taking the absolute value of both equations will yield the same answer. Now all we do is solve for y in both cases

7-y=4; y = 3

and

-7+y=4; y = 11

We can plug both values into the original function to demonstrate this.

$| 7 - \left(3\right) | = 4$

$| 7 - \left(11\right) | = 4$

Both cases are true, and we have two solutions for y