Linear equations are the most tested topic on the SAT Math section. If you can solve these quickly and accurately, you're already ahead of most test-takers.

The 3-Step Method

Every linear equation can be solved with these three steps:

  1. Simplify both sides (distribute, combine like terms)
  2. Move variables to one side, constants to the other
  3. Divide to isolate the variable
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Example 1: Basic

Solve:

Step 1: Already simplified.

Step 2: Subtract 7 from both sides:

Step 3: Divide by 3:

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Example 2: Variables on Both Sides

Solve:

Step 1: Already simplified.

Step 2: Subtract : . Then add 3:

Step 3: Divide by 3:

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Example 3: Distribution Required

Solve:

Step 1: Distribute:

Step 2: Subtract : . Then add 1:

Step 3: Already isolated!

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Common Mistakes to Avoid

  • Forgetting to distribute to ALL terms: , not
  • Sign errors when moving terms: when you move to the other side, it becomes
  • Not checking your answer: always plug it back in!
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SAT Pro Tip

On the SAT, linear equations appear in about 30% of math questions. Speed matters — practice until solving these takes less than 30 seconds each.

Ready to practice? Try our Linear Equations lessons with step-by-step guidance and an AI tutor that helps you learn.