The first step in solving the equation [tex]\(\frac{2}{3} x + \frac{1}{3} x + 2 = 5\)[/tex] is to combine like terms.
Here's a detailed explanation of the first step:
1. Combine like terms: Look at the terms involving [tex]\(x\)[/tex] on the left-hand side of the equation. We have [tex]\(\frac{2}{3} x\)[/tex] and [tex]\(\frac{1}{3} x\)[/tex].
When we combine these like terms, we add the coefficients together:
[tex]\[
\frac{2}{3} x + \frac{1}{3} x = \left(\frac{2}{3} + \frac{1}{3}\right) x = 1x = x
\][/tex]
Therefore, after combining like terms, the equation simplifies to:
[tex]\[
x + 2 = 5
\][/tex]
This is the simplified form after the first step. Now, the equation is easier to solve.
So, the correct first step is to combine like terms.
