Question

2b + 8 - 5b + 3 = -13 + 8b - 5
2x + 7 - 5x + 8 = 3(5 + 6x) - 12
\frac{1}{2}z + 6 = \frac{3}{2}(z + 6)
\frac{1}{9}(2m - 16) = \frac{1}{3}(2m + 4)

Explanation:

Step1: Solve for \( b \) in \( 2b + 8 - 5b + 3 = -13 + 8b - 5 \)

Combine like terms: \( -3b + 11 = 8b - 18 \)
Add \( 3b \) to both sides: \( 11 = 11b - 18 \)
Add 18 to both sides: \( 29 = 11b \)
Divide by 11: \( b = \frac{29}{11} \)

Step2: Solve for \( x \) in \( 2x + 7 - 5x + 8 = 3(5 + 6x) - 12 \)

Combine like terms: \( -3x + 15 = 15 + 18x - 12 \)
Simplify right side: \( -3x + 15 = 18x + 3 \)
Add \( 3x \) to both sides: \( 15 = 21x + 3 \)
Subtract 3: \( 12 = 21x \)
Divide by 21: \( x = \frac{4}{7} \)

Step3: Solve for \( z \) in \( \frac{1}{2}z + 6 = \frac{3}{2}(z + 6) \)

Multiply both sides by 2: \( z + 12 = 3(z + 6) \)
Expand: \( z + 12 = 3z + 18 \)
Subtract \( z \): \( 12 = 2z + 18 \)
Subtract 18: \( -6 = 2z \)
Divide by 2: \( z = -3 \)

Step4: Solve for \( m \) in \( \frac{1}{9}(2m - 16) = \frac{1}{3}(2m + 4) \)

Multiply both sides by 9: \( 2m - 16 = 3(2m + 4) \)
Expand: \( 2m - 16 = 6m + 12 \)
Subtract \( 2m \): \( -16 = 4m + 12 \)
Subtract 12: \( -28 = 4m \)
Divide by 4: \( m = -7 \)

Answer:

\( b = \frac{29}{11} \), \( x = \frac{4}{7} \), \( z = -3 \), \( m = -7 \)