Absolute Value

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.

c. Solve for x.

IxI = 8

x = 8 and x = -8

The solutions are 8 and -8.

Step 3. Check the solutions.