Foundations

Sum of Solutions on the SAT: Desmos Walkthrough

Graph both sides of an equation as separate

y=

curves, click each intersection point, and add the

x

-values to get the sum of the solutions.

This is a Foundations lesson: the core Desmos moves (graphing both sides, plotting points, reading intersections) that every other technique in the course builds on.

Take this lesson interactively

A real SAT-style question

$| - 5 x + 13 | = 73$

What is the sum of the solutions to the given equation?

$- \frac{146}{5}$

$negative 12$

$0$

$StartFraction 26 Over 5 EndFraction$

How to solve it in Desmos, step by step

The idea

Graph each side of the equation, then click the two gray intersection points to read off both solutions and add them.

1
Step 1
Type this. Desmos draws the V-shaped absolute-value graph.
Type in Desmos
$y=\left|-5x+13\right|$
2
Step 2
Type this. Desmos adds the horizontal line and two gray dots appear where it crosses the V.
Type in Desmos
$y=73$
3
Step 3
Click the left gray intersection point. Desmos shows the coordinates (-12, 73), so one solution is x equals -12.
4
Step 4
Click the right gray intersection point. Desmos shows the coordinates (17.2, 73), so the other solution is x equals 17.2.
5
Step 5
Type this to add the two x-values. Desmos displays 5.2, which equals 26 over 5, matching choice D.
Type in Desmos
$-12+17.2$

The answer is D.

$StartFraction 26 Over 5 EndFraction$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

|7x - 9| = 58

What is the sum of the solutions to the given equation?

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson