Module 3 Lesson 16: Graphs Can Solve Equations Too

Warm Up: Solve for x in the following equation: |𝑥 + 2| − 3 = 0.5𝑥 + 1

Let’s try solving using another method!

Let 𝑓(𝑥) = |𝑥 + 2| − 3 and 𝑔(𝑥) = 0.5𝑥 + 1. Use Desmos or a graphing

calculator to graph these two expressions on the same coordinate plane. What do

you see?

Let’s use this same method to solve the following equation:

−|𝑥 − 3| + 4 = |0.5𝑥| − 5

What are the equations for the two expressions you are graphing?

What are the intersection points? What are the solutions to the equation?

−|𝑥 − 3.5| + 4 = −0.25𝑥 − 1

What are the equations of the two expressions you are graphing?

What are the intersection points? What are the solutions to the equation?

When we are doing these problems we are often approximating solutions. Why

does this method find approximate answers instead of exact solutions?

3 − 2𝑥 = |𝑥 − 5| 2(1.5)𝑥 = 2 + 1.5𝑥

Verify the solution sets using the original equations.

Assignment: Problem Set #2(a-d)

For the grade on this assignment, you must:

Sketch a picture of the two graphs, including a label on any intersections

with the x- or y- axis

Label the points of intersection as ordered pairs

Show your work where you are checking the solutions in the equations you

graphed