Backsolving on the SAT

Why the SAT Emphasizes Backsolving

Backsolving takes advantage of multiple choice answers. Instead of building and solving a full equation, you test answer choices until one works.

This lesson shows how to start with a middle answer choice, how to adjust up or down based on the result, and how to confirm your final choice without wasting time.

A Simple Definition Unlocks Backsolving

Plug an answer choice into the original problem statement and see if it satisfies the condition. If it is too large or too small, you can move to a different choice based on that direction.

Backsolving works best when the answer choices are numerical and the algebra looks messy. It is less effective if the choices are expressions, because it becomes hard to compare.

Work Through Backsolving Step by Step

Here is a quick backsolving example so you can see how to test an answer choice efficiently.

Use Desmos to Check Backsolving

Desmos can help test choices quickly, but backsolving is mostly mental. Use Desmos if the calculations are heavy.

The speed comes from choice testing, not the calculator.

Desmos is faster when the arithmetic is heavy or when you want to test several choices quickly. Algebra is faster when the equation is simple enough to solve directly.

Expert move: After you translate the problem, graph left and right sides or test candidate values quickly in Desmos; keep only values that fit the context.

When to skip Desmos: If a quick algebra step or estimation settles it, solve by hand and use Desmos only to verify.

• Desmos features used: quick arithmetic checks.
• Common mistake: testing a value but forgetting to use the original equation.

Practice Backsolving with SAT-Style Questions

Use answer choices as your inputs.

Key Takeaways to Remember for Backsolving

• Use answer choices as test inputs to avoid heavy algebra.
• Start with a middle choice to cut the search quickly.
• Always test in the original equation.