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Solve for $v$ . $\newline$ $\frac{1}{2}v + 8 = 3 - \frac{1}{3}v$ $\newline$ $v =$ __

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

v

.

\newline

\frac{1}{2}v + 8 = 3 - \frac{1}{3}v

\newline

v =

__

Combine like terms: Combine like terms by getting all $v$ terms on one side and constants on the other. $\frac{1}{2}v + \frac{1}{3}v + 8 = 3$ Combine the $v$ terms: $\left(\frac{1}{2} + \frac{1}{3}\right)v + 8 = 3$ To add $\frac{1}{2}$ and $\frac{1}{3}$ , find a common denominator, which is $6$ : $\left(\frac{3}{6} + \frac{2}{6}\right)v + 8 = 3$ $\left(\frac{5}{6}\right)v + 8 = 3$
Isolate the v term: Isolate the v term by subtracting $8$ from both sides. $\newline$ $(\frac{5}{6})v + 8 - 8 = 3 - 8$ $\newline$ $(\frac{5}{6})v = -5$
Solve for $v$ : Solve for $v$ by dividing both sides by $\frac{5}{6}$ . $\frac{\left(\frac{5}{6}\right)v}{\left(\frac{5}{6}\right)} = \frac{-5}{\left(\frac{5}{6}\right)}$ $v = -5 \times \left(\frac{6}{5}\right)$ $v = -6$

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