Question

consider the equation \\(\frac{5}{3}v + 4 + \frac{1}{3}v = 8\\). what is the resulting equation after the first step in the solution?\
\\(\frac{5}{3}v + 4 = 8 - \frac{1}{3}v\\)\
\\(2v + 4 = 8\\)\
\\(4 + v = 8 - \frac{5}{3}v\\)\
\\(\frac{4}{3}v + 4 = 8\\)

Explanation:

Step1: Combine like terms

The original equation is \(\frac{5}{3}v + 4+\frac{1}{3}v = 8\). The like terms for \(v\) are \(\frac{5}{3}v\) and \(\frac{1}{3}v\). Combining them, we have \(\frac{5}{3}v+\frac{1}{3}v=\frac{5 + 1}{3}v=\frac{6}{3}v = 2v\). So substituting back into the equation, we get \(2v+4 = 8\).

Answer:

\(2v + 4 = 8\) (the second option)