Solve SAT Absolute Value Equations with Desmos
Absolute value equations usually have two answers and trip students up. Graph both sides in Desmos and read off the intersections.
Step by step
- 1
Type the absolute value with bars
Enter the equation using | | — e.g. y = |2x − 3|. Desmos draws the V-shape.
- 2
Graph the other side too
Type the right-hand side as its own line — e.g. y = 5, a horizontal line.
- 3
Click both intersections
An absolute value usually meets a horizontal line at TWO points. Click each — the x-values are your two solutions.
- 4
Watch for 0, 1, or 2 solutions
If the line is below the V's tip, there's no solution; right at the tip, exactly one; above it, two.
- 5
Answer the question
Read the x-coordinates of the intersection points.
Pro tip
You can also solve it the one-line way: graph y = |2x − 3| − 5 and read the two x-intercepts. Either method gives both answers without splitting into cases.
Try it yourself
Work the example right here in a live Desmos calculator — no Bluebook needed.
Solve |2x − 3| = 5.
Graph both and click the two intersection points — the x-values are your solutions.
Loading interactive calculator…
Show the answer
Answer: x = 4 or x = −1
Graph y = |2x − 3| and y = 5; they meet at (4, 5) and (−1, 5), so x = 4 or x = −1. (Algebra check: 2x − 3 = 5 → x = 4; 2x − 3 = −5 → x = −1.)
Put the trick to work on a real test
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