Let's solve each equation step by step.
1. \(7 - (5r - 13) = -15\)
First, distribute the negative sign: \[ 7 - 5r + 13 = -15 \] Combine like terms on the left: \[ 20 - 5r = -15 \] Subtract 20 from both sides: \[ -5r = -15 - 20 \] \[ -5r = -35 \] Divide by -5: \[ r = 7 \]
2. \(3 - (7p + 5) = 27\)
Distribute the negative sign: \[ 3 - 7p - 5 = 27 \] Combine like terms on the left: \[ -7p - 2 = 27 \] Add 2 to both sides: \[ -7p = 27 + 2 \] \[ -7p = 29 \] Divide by -7: \[ p = -\frac{29}{7} \]
3. \(-15b + 21 + 5b = -19\)
Combine like terms: \[ -15b + 5b + 21 = -19 \] \[ -10b + 21 = -19 \] Subtract 21 from both sides: \[ -10b = -19 - 21 \] \[ -10b = -40 \] Divide by -10: \[ b = 4 \]
4. \(-130 = -5(3x + 3) + 5\)
Distribute the -5: \[ -130 = -15x - 15 + 5 \] Combine like terms on the right: \[ -130 = -15x - 10 \] Add 10 to both sides: \[ -130 + 10 = -15x \] \[ -120 = -15x \] Divide by -15: \[ x = \frac{120}{15} = 8 \]
5. \(5(y + 2) - (y - 1) = 3\)
Distribute the 5 and the negative sign: \[ 5y + 10 - y + 1 = 3 \] Combine like terms: \[ 4y + 11 = 3 \] Subtract 11 from both sides: \[ 4y = 3 - 11 \] \[ 4y = -8 \] Divide by 4: \[ y = -2 \]
6. \(-20 = -4x - 6x\)
Combine like terms: \[ -20 = -10x \] Divide by -10: \[ x = \frac{20}{10} = 2 \]
Summary of Solutions:
- \( r = 7 \)
- \( p = -\frac{29}{7} \)
- \( b = 4 \)
- \( x = 8 \)
- \( y = -2 \)
- \( x = 2 \)
If you have any more equations or need further assistance, let me know!