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Solve for $b$ . $\newline$ $b + 3 = \frac{1}{2}(b - 4)$ $\newline$ b = ____

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

b

.

\newline

b + 3 = \frac{1}{2}(b - 4)

\newline

b = ____

Distribute $\frac{1}{2}$ to terms: Distribute $\frac{1}{2}$ to the terms inside the parentheses in the equation $b + 3 = \frac{1}{2}(b - 4)$ . $\newline$ Calculation: $\newline$ $\frac{1}{2}(b - 4) = \frac{1}{2} \times b - \frac{1}{2} \times 4$ $\newline$ $= \frac{1}{2} b - 2$ $\newline$ Rewritten equation: $b + 3 = \frac{1}{2} b - 2$
Get all $b$ terms: Get all $b$ terms on one side by subtracting $\frac{1}{2} b$ from both sides. $\newline$ Calculation: $\newline$ $b + 3 - \frac{1}{2} b = \frac{1}{2} b - 2 - \frac{1}{2} b$ $\newline$ $\frac{1}{2} b + 3 = -2$

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