Absolute Value
Absolute Value Functions
Solving Equations
When solving absolute value equations algebraically, the x needs to be isolated. However, because the x is inside the absolute value bars, there are additional steps needed. For example, what is the solution for IxI = 3? This is asking, what values are a distance of three units from zero. There are actually two solutions. X can be substituted by 3 because I3I =3, but x can also be substituted by -3 because I-3I is equal to 3. Both numbers are 3 units away from zero on the number line. Therefore, most absolute value equations will have two solutions.
To solve, IxI + 2 = 10, use the following steps:
Step 1. Isolate the absolute value bars using inverse operations.
|x| + 2 - 2 = 10 - 2
|x| = 8
Step 2. Write two equations.
a. Write one equation to equal the positive.
b. Write the other equation to equal the negative.
b. Write the other equation to equal the negative.
c. Solve for x.
IxI = 8
x = 8 and x = -8
The solutions are 8 and -8.
Step 3. Check the solutions.
