Linear Equations • Topic 3 of 6

Multi-Step Equations

Multi-step equations may require distributing over brackets and combining like terms before you isolate the variable. The reliable order is: distribute, combine like terms on each side, then use inverse operations to get the variable alone. For 2(x + 3) = 14, distribute to 2x + 6 = 14, subtract 6, then divide by 2. Watch signs when distributing a negative. These equations appear constantly in SAT word problems, where translating the situation produces brackets and several terms; a clean, ordered approach prevents errors and keeps the work fast.

✅ Solved examples

1. Solve 2(x + 3) = 14.
Distribute: 2x + 6 = 14; subtract 6: 2x = 8; divide: x = 4.
2. Solve 3x + 2x = 25.
Combine like terms: 5x = 25; divide: x = 5.
3. Solve 4(x − 1) = 12.
Distribute: 4x − 4 = 12; add 4: 4x = 16; divide: x = 4.
4. Solve 5x − 3 + 2x = 18.
Combine: 7x − 3 = 18; add 3: 7x = 21; divide: x = 3.

✏️ Practice — try these, take hints as needed

1. Solve 3(x + 2) = 21.
Distribute: 3x + 6.
Subtract 6: 3x = 15.
Divide by 3.
5.
2. Solve 4x + 3x = 35.
Combine like terms.
7x = 35.
Divide by 7.
5.
3. Solve 2(x − 4) = 6.
Distribute: 2x − 8.
Add 8: 2x = 14.
Divide by 2.
7.
4. Solve 6x − 2 − 2x = 14.
Combine: 4x − 2.
Add 2: 4x = 16.
Divide by 4.
4.
5. Solve 5(x + 1) = 30.
Distribute: 5x + 5.
Subtract 5: 5x = 25.
Divide by 5.
5.

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
← Two-Step Equations Variables on Both Sides →