Question

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

Answer 1

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
`-(7-y) = 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-(3)| = 4`

`|7-(11)|=4`

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