Perfect1600

Digital SAT · Solve it in Desmos

How to Solve Linear Equations on Desmos (Digital SAT)

Desmos solves any one-variable equation on the spot, ideal on grid-ins. Word problems still need you to build the equation first; once written, the calculator finishes it. Solve fully by hand only for unknown coefficients or a rearrange-for-a-variable prompt.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for linear equations

The Desmos steps

  1. 1

    Type the equation with x

    Enter the whole equation using x, like 5(x-2)=3x+16.

  2. 2

    Read the marked solution

    Desmos draws a vertical line at the x that makes it true; that is the solution.

  3. 3

    Finish the asked quantity

    If a quantity built from x is wanted, compute it in Desmos once you have x.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
If x−15=42x - 15 = 42, what is the value of xx?
A
2727
B
4242
5757
D
630630

A: Incorrect. This subtracts 15 instead of adding it: 42−15=2742-15=27.

B: Incorrect. This ignores the −15-15 and just reports the right side, 42.

C: Correct. Add 15 to both sides: x=42+15=57x=42+15=57.

D: Incorrect. This multiplies 42 by 15 instead of adding: 42×15=63042\times15=630.

Explanation

The 15 is subtracted from xx, so add 15 to both sides: x=42+15=57x=42+15=57.

Medium example
If 5(x−2)=3x+165(x - 2) = 3x + 16, what is the value of xx?
A
33
B
99
1313
D
2626

A: Incorrect. This moves the constants with the wrong signs: 2x=16−10=62x=16-10=6, giving x=3x=3.

B: Incorrect. This distributes the 5 only to xx: 5x−2=3x+165x-2=3x+16 gives x=9x=9.

C: Correct. Distribute and solve: 5x−10=3x+16⇒2x=26⇒x=135x-10=3x+16\Rightarrow 2x=26\Rightarrow x=13.

D: Incorrect. This reaches 2x=262x=26 but forgets to divide by 2.

Explanation

Distribute the 5: 5x−10=3x+165x-10=3x+16. Collect terms: 2x=262x=26. Divide by 2: x=13x=13.

Hard example
The sum of three consecutive multiples of 5 is 90. What is the greatest of the three multiples?
A
20
B
25
C
30
35

A: Incorrect. This computes one multiple below the smallest, an off-by-one error: 20.

B: Incorrect. This reports the smallest of the three multiples instead of the greatest: 25.

C: Incorrect. This reports the middle of the three multiples instead of the greatest: 30.

D: Correct. Letting the smallest be nn, n+(n+5)+(n+10)=90n+(n+5)+(n+10)=90 gives 3n+15=903n+15=90, so n=25n=25; the multiples are 25, 30, 35, and the greatest is 35.

Explanation

Letting the smallest be n, 3n + 15 = 90 gives n = 25, so the multiples are 25, 30, 35, and the greatest is 35.

Try it with the calculator

Question 1easy

If 6x=546x = 54, what is the value of xx?

Question 2easy

If 2x+3=152x + 3 = 15, what is the value of xx?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

Start the free diagnostic

Desmos questions

Can Desmos solve linear equations questions on the SAT?

Desmos solves any one-variable equation on the spot, ideal on grid-ins. Word problems still need you to build the equation first; once written, the calculator finishes it. Solve fully by hand only for unknown coefficients or a rearrange-for-a-variable prompt.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master linear equations, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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