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

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

v

.

\newline

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

\newline

v = ____

Distribute $2$ : Distribute $2$ into the parentheses. $\newline$ $2 \times 3 - 2 \times \left(\frac{1}{4}\right)v = 2 - v$ $\newline$ $6 - \frac{1}{2}v = 2 - v$
Add $\frac{1}{2}v$ : Add $\frac{1}{2}v$ to both sides to start isolating $v$ . $\newline$ $6 - \frac{1}{2}v + \frac{1}{2}v = 2 - v + \frac{1}{2}v$ $\newline$ $6 = 2 - \frac{1}{2}v$
Subtract $2$ : Subtract $2$ from both sides to simplify. $\newline$ $6 - 2 = 2 - \frac{1}{2}v - 2$ $\newline$ $4 = -\frac{1}{2}v$
Multiply by $-2$ : Multiply both sides by $-2$ to solve for $v$ . $-2 \times 4 = -2 \times (-\frac{1}{2}v)$ $-8 = v$

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