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

Question

1913 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-04T00:23:09

y = 3 and y = 11

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

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