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Consider the equation [tex]\frac{5}{3} v + 4 + \frac{1}{3} v = 8[/tex]. What is the resulting equation after the first step in the solution?

A. [tex]\frac{5}{3} v + 4 = 8 - \frac{1}{3} v[/tex]
B. [tex]\frac{4}{3} v + 4 = 8[/tex]
C. [tex]4 + v = 8 - \frac{5}{3} v[/tex]
D. [tex]2v + 4 = 8[/tex]


Sagot :

To solve the equation [tex]\(\frac{5}{3}v + 4 + \frac{1}{3}v = 8\)[/tex], we first want to simplify and combine like terms on the left-hand side.

1. Combine the terms involving [tex]\(v\)[/tex]:
[tex]\[ \frac{5}{3}v + \frac{1}{3}v = \left(\frac{5}{3} + \frac{1}{3}\right)v = \frac{6}{3}v = 2v \][/tex]

2. Now substitute [tex]\(2v\)[/tex] back into the equation:
[tex]\[ 2v + 4 = 8 \][/tex]

The resulting equation after the first step in solving is:
[tex]\[ 2v + 4 = 8 \][/tex]