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.