What are Absolute Value Equations

Absolute Value Equations are equations that look like this:

I x + 5 I = 15

They have 2 solutions almost all the time. To solve this equation we do this:

x+5=15 x+5=-15

Then you solve them:

x+5=15 x+5=-15

x=15-5 x=-15-5

x=10 x=-20

The solutions would be x=10 and x=-20.

In some cases, you only have one solution:

I x + 5 I = 0

0 cannot be negative, so we only have one equation to solve:

x+5=0

x=0-5

x=-5

The one solution would be x=-5.

In some OTHER cases, you have no solution. This happens when the absolute value equation equals to a negative number:

I x + 5 I = -10

Absolute value solutions are always going to end up positive because absolute value turns the number, negative or positive, into a positive.