To find an equivalent expression for [tex]\(\frac{1}{2}(2a - 6b + 8)\)[/tex] in its simplest form, follow these steps:
1. Distribute [tex]\(\frac{1}{2}\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(\frac{1}{2}\)[/tex] by the first term, [tex]\(2a\)[/tex]:
[tex]\[
\frac{1}{2} \cdot 2a = a
\][/tex]
- Multiply [tex]\(\frac{1}{2}\)[/tex] by the second term, [tex]\(-6b\)[/tex]:
[tex]\[
\frac{1}{2} \cdot (-6b) = -3b
\][/tex]
- Multiply [tex]\(\frac{1}{2}\)[/tex] by the third term, [tex]\(8\)[/tex]:
[tex]\[
\frac{1}{2} \cdot 8 = 4
\][/tex]
2. Combine all the results from each multiplication:
- Combine [tex]\(a\)[/tex], [tex]\(-3b\)[/tex], and [tex]\(4\)[/tex] to form the final equivalent expression:
[tex]\[
a - 3b + 4
\][/tex]
Thus, the equivalent expression with the fewest symbols possible is:
[tex]\[
a - 3b + 4
\][/tex]
