Let's solve each equation step by step:
Question 1: Solve \(6y + 12 = 48\).
- Subtract 12 from both sides: \[ 6y = 48 - 12 \] \[ 6y = 36 \]
- Divide both sides by 6: \[ y = \frac{36}{6} = 6 \]
Answer: 6
Question 2: Solve \(8x - 11 = 77\).
- Add 11 to both sides: \[ 8x = 77 + 11 \] \[ 8x = 88 \]
- Divide both sides by 8: \[ x = \frac{88}{8} = 11 \]
Answer: 11
Question 3: Solve \(7 + 4x = 55\).
- Subtract 7 from both sides: \[ 4x = 55 - 7 \] \[ 4x = 48 \]
- Divide both sides by 4: \[ x = \frac{48}{4} = 12 \]
Answer: 12
Question 4: Solve \(\frac{m}{4} - 6 = 2\).
- Add 6 to both sides: \[ \frac{m}{4} = 2 + 6 \] \[ \frac{m}{4} = 8 \]
- Multiply both sides by 4: \[ m = 8 \times 4 = 32 \]
Answer: 32
Question 5: Solve \(12 + \frac{m}{4} = 14\).
- Subtract 12 from both sides: \[ \frac{m}{4} = 14 - 12 \] \[ \frac{m}{4} = 2 \]
- Multiply both sides by 4: \[ m = 2 \times 4 = 8 \]
Answer: 8
Question 6: Solve \(8y + 9 = 65\).
- Subtract 9 from both sides: \[ 8y = 65 - 9 \] \[ 8y = 56 \]
- Divide both sides by 8: \[ y = \frac{56}{8} = 7 \]
Answer: 7
Question 7: Solve \(9x - 12 = 60\).
- Add 12 to both sides: \[ 9x = 60 + 12 \] \[ 9x = 72 \]
- Divide both sides by 9: \[ x = \frac{72}{9} = 8 \]
Answer: 8
Question 8: Solve \(4 + 4x = 48\).
- Subtract 4 from both sides: \[ 4x = 48 - 4 \] \[ 4x = 44 \]
- Divide both sides by 4: \[ x = \frac{44}{4} = 11 \]
Answer: 11
Question 9: Solve \(\frac{m}{3} - 4 = 8\).
- Add 4 to both sides: \[ \frac{m}{3} = 8 + 4 \] \[ \frac{m}{3} = 12 \]
- Multiply both sides by 3: \[ m = 12 \times 3 = 36 \]
Answer: 36
Question 10: Solve \(10 + \frac{m}{6} = 12\).
- Subtract 10 from both sides: \[ \frac{m}{6} = 12 - 10 \] \[ \frac{m}{6} = 2 \]
- Multiply both sides by 6: \[ m = 2 \times 6 = 12 \]
Answer: 12
Summary of Answers:
- 6
- 11
- 12
- 32
- 8
- 7
- 8
- 11
- 36
- 12