- Given: 4(x + y) = 48, y = 6. Prove: x = 6.
- Substitute y = 6 into the equation: 4(x + 6) = 48.
- Divide both sides by 4: x + 6 = 12.
- Subtract 6 from both sides: x = 6.
- Given: 5x - 3 = 52. Prove: x = 11.
- Add 3 to both sides: 5x = 55.
- Divide both sides by 5: x = 11.
- Given: -3 + x/3 = -13. Prove: x = -30.
- Add 3 to both sides: x/3 = -10.
- Multiply both sides by 3: x = -30.
- Given: 2(4 - x) - 5x = 78. Prove: x = -10.
- Distribute the 2: 8 - 2x - 5x = 78.
- Combine like terms: 8 - 7x = 78.
- Subtract 8 from both sides: -7x = 70.
- Divide both sides by -7: x = -10.
- Given: 5x - 21 = -2x + 28. Prove: x = 7.
- Add 2x to both sides: 7x - 21 = 28.
- Add 21 to both sides: 7x = 49.
- Divide both sides by 7: x = 7.
- Given: 4(2x - 8) = (1/7)(49x + 70) + 2. Prove: x = 44.
- Distribute on both sides: 8x - 32 = 7x + 10 + 2.
- Simplify the right side: 8x - 32 = 7x + 12.
- Subtract 7x from both sides: x - 32 = 12.
- Add 32 to both sides: x = 44.
Parent Tip: Review the logic above to help your child master the concept of algebraic proof worksheets.
