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

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

b

.

\newline

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

\newline

b =

__

Distribute $\frac{1}{4}$ : Distribute $\frac{1}{4}$ to the terms inside the parentheses. $\newline$ Calculation: $\frac{1}{4} \times (3b + 2) = (\frac{1}{4} \times 3b) + (\frac{1}{4} \times 2) = \frac{3}{4}b + \frac{1}{2}$
Set equation sides: Set the equation with all terms involving $b$ on one side and constants on the other. $\newline$ Calculation: $b + 1 = \frac{3}{4}b + \frac{1}{2}$ $\newline$ $b - \frac{3}{4}b = \frac{1}{2} - 1$
Combine like terms: Simplify the equation by combining like terms. $\newline$ Calculation: $\frac{1}{4}b = -\frac{1}{2}$
Isolate and solve for $b$ : Solve for $b$ by isolating $b$ . $\newline$ Calculation: $b = \frac{-1}{2} / \frac{1}{4}$ $\newline$ b = $-2$

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