🧱 See It
Two-step equations already taught the two undo moves: subtract/add first, then multiply/divide. Now some equations hide an extra step at the very start — a bracket that needs to be distributed before those two familiar moves can even begin. Every term inside the brackets gets multiplied by the number sitting right outside them.
Sometimes distributing leaves two matching terms on the same side — say two separate x terms. When that happens there's one more tidy-up step: collect like terms (add the matching terms together) so the side is as simple as possible before the undo moves begin.
✏️ Draw It
Solve 3(x + 2) = 15. The 3 outside the brackets multiplies both terms inside — draw both arrows before combining anything:
3 × x = 3x and 3 × 2 = 6 — both arrows fire before anything gets combined, giving 3x + 6 = 15.
🔢 Write It
3(x + 2) = 15
Step 1 — distribute the 3:
3x + 6 = 15
Step 2 — undo the addition (subtract 6 from both sides):
3x = 9
Step 3 — undo the multiplication (divide both sides by 3):
x = 3
💡 Worked Examples
Example 1: 2(x − 4) = 10
- Distribute the 2:
2x − 8 = 10 - Add 8 to both sides:
2x = 18 - Divide both sides by 2:
x = 9 - Verify:
2(9 − 4) = 2 × 5 = 10✓
Example 2: −3(x + 1) = 12
- Distribute the −3:
−3x − 3 = 12 - Add 3 to both sides:
−3x = 15 - Divide both sides by −3:
x = −5 - Verify:
−3(−5 + 1) = −3 × −4 = 12✓
Example 3 — distributing leaves like terms to collect: 3(x + 2) + 2x = 16
- Distribute the 3:
3x + 6 + 2x = 16 - Collect like terms — add the two
xterms (3x + 2x = 5x):5x + 6 = 16 - Subtract 6 from both sides:
5x = 10 - Divide both sides by 5:
x = 2 - Verify:
3(2 + 2) + 2 × 2 = 12 + 4 = 16✓