To simplify the expression [tex]\(\frac{1}{3} - 7a + \frac{2}{3}\)[/tex], we need to combine like terms. In this case, the like terms are the constants [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]. The term [tex]\(-7a\)[/tex] stands alone because it does not have a like term to combine with.
Here's the step-by-step process:
1. Identify the like terms:
The terms [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex] are both constants, so they are like terms and can be combined. The term [tex]\(-7a\)[/tex] is the only term containing the variable [tex]\(a\)[/tex], and there are no other [tex]\(a\)[/tex]-terms to combine it with.
2. Combine the constants:
Add [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{1}{3} + \frac{2}{3} = \frac{1+2}{3} = \frac{3}{3} = 1
\][/tex]
3. Rewrite the expression:
Substitute the combined constant back into the expression, along with the [tex]\(-7a\)[/tex] term:
[tex]\[
1 - 7a
\][/tex]
This is the simplified form of the given algebraic expression.
Thus, [tex]\(\frac{1}{3} - 7a + \frac{2}{3}\)[/tex] simplifies to:
[tex]\[
1 - 7a
\][/tex]
