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How to Solve SAT Linear Inequalities with Desmos

Last updated: October 2, 2026

Type the inequality into Desmos exactly as the question prints it. Desmos shades every value that makes it true, draws the boundary dashed or solid to match the sign, and never asks you to flip the sign by hand. Your job is to find the exact edge of the shading and say which side of it the answer is on.

The problem

Solve: 2x − 1 > 5
Solution: x > 3

The boundary is where the two sides are equal: 2x − 1 = 5, at x = 3. The answer is every x on the side of it where the left side is bigger. Desmos shows you both.

What do you type?

One row: 2x − 1 > 5

Desmos shades everything to the right of a vertical line at x = 3, and the line is dashed. The dashed line is the boundary. The shading is the answer: x > 3.

You do not have to get x alone first. Desmos graphs the inequality as printed, with x on both sides if that is how the question wrote it.

How do you get the exact boundary?

The edge of the shading shows you about where the boundary is. To get the exact number, graph the two sides as separate rows:

y = 2x − 1
y = 5

Click where the lines cross and Desmos labels the point (3, 5). Its x-coordinate, 3, is the boundary. Now read the direction: right of x = 3, the line y = 2x − 1 sits above y = 5. Above means bigger, and bigger is what > asked for. So x > 3.

That is the graph-both-sides move from solving linear equations in Desmos, plus one question: which side.

Dashed or solid?

Desmos draws the boundary the way the sign says:

• < or >: dashed. The boundary value is not a solution.
• ≤ or ≥: solid. The boundary value is a solution.

Type >= and Desmos turns it into ≥. Change the row to 2x − 1 ≥ 5 and the line goes solid.

That line style is the difference between x > 3 and x ≥ 3, and the SAT puts both in the answer choices. If the question asks for the smallest integer that works, x > 3 gives you 4 and x ≥ 3 gives you 3. Look at the line before you pick.

Why don't you flip the sign in Desmos?

By hand, dividing by a negative flips the inequality. Missing that flip is where most points on this skill go.

Desmos does not divide anything. Multiply the problem through by −1 and you get 1 − 2x < −5. Type that, and Desmos shades the same region: x > 3. The flip is already in the picture. If your hand-solved answer points the other way from the shading, trust the shading and find the step where you divided.

Why the sign flips, and how to set up the inequality from a word problem, is the strategy side of this skill. SAT Linear Inequalities covers it.

What about two variables and systems?

Swap the 5 for y. Type y > 2x − 1 and Desmos shades everything above a dashed line. Add y < 5 on the next row and it shades below a dashed horizontal line in a second color. Where the two colors overlap, the shading is darker. That darker region is the solution to the system, and its corner is the same (3, 5) you clicked earlier.

When the question asks which point is a solution, type each answer choice as a point on its own row. Try (0, 2): it lands in the darker region, so it works. A point outside the overlap, or sitting on a dashed edge, does not.

How do you practice this?

Take 10 inequality questions from practice tests: some in one variable, some in two, a few systems. For each one:

1. Type it exactly as printed and look at where the shading sits
2. Graph both sides as separate lines and click the crossing to get the exact boundary
3. Say out loud which side and whether the edge is dashed or solid, before you look at the choices

When your hand answer and the shading disagree, write down which step broke. It is almost always the sign flip or the edge.

HIROSCORE tracks your accuracy on linear inequalities as its own skill, separately from the rest of Algebra, so a run of wrong-side answers shows up as what it is instead of hiding inside a math score that looks fine. The GPS for your SAT score.