Linear Equations • Topic 1 of 6

One-Step Equations

A one-step equation is solved with a single inverse operation. If something is added to the variable, subtract it from both sides; if the variable is multiplied by a number, divide both sides by that number. The guiding idea is balance: whatever you do to one side you must do to the other, keeping the equation true. Always undo the operation that is attached to the variable. A quick check — substitute your answer back into the original equation — confirms the solution and catches arithmetic slips, which is worth the few seconds on the SAT.

✅ Solved examples

1. Solve x + 7 = 12.
Subtract 7 from both sides: x = 5.
2. Solve 3x = 21.
Divide both sides by 3: x = 7.
3. Solve x − 4 = 10.
Add 4 to both sides: x = 14.
4. Solve x/5 = 6.
Multiply both sides by 5: x = 30.

✏️ Practice — try these, take hints as needed

1. Solve x + 9 = 15.
Undo the +9.
Subtract 9 from both sides.
15 − 9.
6.
2. Solve 4x = 28.
Undo the ×4.
Divide both sides by 4.
28 ÷ 4.
7.
3. Solve x − 6 = 3.
Undo the −6.
Add 6 to both sides.
3 + 6.
9.
4. Solve x/3 = 8.
Undo the ÷3.
Multiply both sides by 3.
8 × 3.
24.
5. Solve −2x = 10.
Divide both sides by −2.
10 ÷ (−2).
Mind the sign.
−5.

📝 Topic test — 8 questions

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