Multi-step Equations — SAT Math Explained
Equations that require more than one operation to solve, often involving distribution, combining like terms, and working across both sides of the equals sign.
The Core Idea
The same balance principle applies, but now you must first simplify before you can isolate the variable. Order of steps matters — simplify first, then isolate.
Key Vocabulary
Terms with the same variable raised to the same power — they can be combined (3x + 5x = 8x)
a(b + c) = ab + ac — multiply the outside term by each term inside the parentheses
Adding or subtracting terms that are alike to reduce the number of terms
To get the variable alone on one side of the equation
Step-by-Step: How to Approach Multi-step Equations
Distribute any parentheses on either side
Combine all like terms on each side separately
Move variable terms to the left side (or whichever you prefer)
Move constants to the right side
Divide by the coefficient
Verify your answer
Strategy Insights
When variables appear on both sides, move the smaller coefficient to the other side to keep numbers positive
If you see a fraction as a coefficient, multiplying both sides by the denominator early can clear it
Always check: does your answer make sense in context if it's a word problem?
Real World Application
Splitting a restaurant bill with tip, calculating total cost with tax, or figuring out how many hours to work to afford something
Common Errors to Avoid
Distributing incorrectly, especially with negative signs: -(x + 3) = -x - 3, not -x + 3
Combining unlike terms (e.g., trying to add 3x + 5 as if it were one term)
Moving a term without changing its sign
Practice: Multi-step Equations
5 SAT-style questions. Select your answer and get an instant explanation.
Solve: 2x + 3 - x = 9
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