Solving Absolute Value Equations Graphically

• Recall the steps used to solve an equation graphically:

1) Move all terms to the left hand side of the equation. Call this expression on the left y1

2) Graph y1 and determine the x-intercepts.

3) The x-values of the x-intercepts are the solutions to the equation.

• This will be our approach to solving absolute value equations.

• Example

Solve the following absolute value equation graphically:

2 7 3 2x

Move all terms to the left hand side.

2 7 3 2 0x

Let y1 equal the left hand side.

1y

2 7 3 2 0x Enter the expression for y1 into the calculator

1y

Press Zoom-6 to graph

Use Trace to find the x-intercepts

Absolute value (abs) is the first item in the catalog list (above the 0 key)

Press Trace and then enter 3.

Now repeat the process with x = 4, the intercept on the right.

Since the y-value is 0, (3,0) is an x-intercept, and 3 is a solution to the equation.

Again, the y-value is 0.

The solutions to the equation are x = 3,4