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{4}{3}v + 4 = 8\\) \\(2v + 4 = 8\\) \\(4 + v = 8 - \frac{5}{3}v\\) \\(\frac{5}{3}v + 4 = 8 - \frac{1}{3}v\\)

Explanation:

Step1: Identify like terms

The terms with \( v \) are \( \frac{5}{3}v \) and \( \frac{1}{3}v \).

Step2: Combine like terms

Add \( \frac{5}{3}v \) and \( \frac{1}{3}v \): \( \frac{5}{3}v+\frac{1}{3}v=\frac{5 + 1}{3}v=\frac{6}{3}v = 2v \).
Substitute back into the original equation \( \frac{5}{3}v + 4+\frac{1}{3}v = 8 \), we get \( 2v+4 = 8 \).

Answer:

B. \( 2v + 4 = 8 \)