Final answer:
To solve the equation 1/2b + 4 = 1/8b + 88, we subtract 1/8b and 4 from both sides, combine like terms, and then solve for b which gives us the solution b = 224.
Step-by-step explanation:
To solve the equation 1/2b + 4 = 1/8b + 88, start by combining like terms. To do this, get all the terms with b on one side of the equation and the constant terms on the other side. Subtract 1/8b from both sides to combine the b terms and subtract 4 from both sides to move the constants:
- 1/2b - 1/8b = 88 - 4
- Subtract the fractions by finding a common denominator, which would be 8 in this case:
- (4/8)b - (1/8)b = 84
- (3/8)b = 84
- Multiply both sides by the reciprocal of the coefficient of b to solve for b:
- 8/3 × (3/8)b = 8/3 × 84
- b = 224
If we were solving for a different variable, like y, and had a y term in the denominator, we would first isolate the y term by moving all other terms to the other side of the equation and then multiply both sides by the reciprocal of the coefficient of y.