🧱 See It
Recall the two-step equation moves: undo addition/subtraction first, then undo the coefficient. Nothing changes when that coefficient is a fraction or decimal instead of a whole number — except HOW you undo it. To undo multiplying by a fraction, multiply both sides by its reciprocal (flip it), reusing the fraction-division rule from Level 3.
✏️ Draw It
Solve 1/2 x + 3 = 7:
| Step | Equation |
|---|---|
| Start | 1/2 x + 3 = 7 |
| Subtract 3 from both sides | 1/2 x = 4 |
| Multiply both sides by 2 (the reciprocal of 1/2) | x = 8 |
🔢 Write It
1/2 x + 3 = 7 ⇒ 1/2 x = 4 ⇒ x = 4 × 2 = 8
Fraction coefficient: multiply both sides by its reciprocal. Decimal coefficient: divide normally, exactly like any other two-step equation.
💡 Worked Examples
Example 1 — Fraction coefficient: 2/3 x + 1 = 5
- Subtract 1 from both sides:
2/3 x = 4 - Multiply both sides by the reciprocal,
3/2:x = 4 × 3/2 = 12/2 = 6 - Verify:
2/3(6) + 1 = 4 + 1 = 5✓
Example 2 — Decimal coefficient: 0.25x − 3 = 2
- Add 3 to both sides:
0.25x = 5 - Divide both sides by 0.25:
x = 20 - Verify:
0.25(20) − 3 = 5 − 3 = 2✓
🧠 Quick Reference
Same two moves as always: undo addition/subtraction first, then undo the coefficient. Fraction coefficient? Multiply both sides by its RECIPROCAL. Decimal coefficient? Divide normally — or convert to a fraction first if that's easier.