Linear Equations • Topic 2 of 6

Two-Step Equations

A two-step equation needs two inverse operations, undone in reverse order of operations: first add or subtract to clear the constant, then multiply or divide to clear the coefficient. For 3x + 5 = 20, subtract 5 to get 3x = 15, then divide by 3 to get x = 5. Keeping the equation balanced at each step is essential. Negative coefficients and constants are common traps, so track signs carefully. As always, substituting the answer back verifies it. Two-step equations are the workhorse of SAT algebra word problems.

✅ Solved examples

1. Solve 2x + 3 = 11.
Subtract 3: 2x = 8; divide by 2: x = 4.
2. Solve 5x − 4 = 16.
Add 4: 5x = 20; divide by 5: x = 4.
3. Solve x/2 + 1 = 5.
Subtract 1: x/2 = 4; multiply by 2: x = 8.
4. Solve 3x + 7 = 1.
Subtract 7: 3x = −6; divide by 3: x = −2.

✏️ Practice — try these, take hints as needed

1. Solve 4x + 5 = 21.
Subtract 5 first.
4x = 16.
Divide by 4.
4.
2. Solve 3x − 2 = 13.
Add 2.
3x = 15.
Divide by 3.
5.
3. Solve x/3 + 4 = 9.
Subtract 4.
x/3 = 5.
Multiply by 3.
15.
4. Solve 2x + 9 = 3.
Subtract 9.
2x = −6.
Divide by 2.
−3.
5. Solve 6x − 1 = 17.
Add 1.
6x = 18.
Divide by 6.
3.

📝 Topic test — 8 questions

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