To combine like terms and create an equivalent expression for
[tex]\[
-\frac{1}{2}(-3 y + 10)
\][/tex]
we will perform the following steps:
### Step 1: Distribute the Coefficient
Distribute the [tex]\(-\frac{1}{2}\)[/tex] across each term inside the parentheses [tex]\(-3y + 10\)[/tex].
### Step 2: Multiply each term
Let's perform the multiplication:
1. Multiply [tex]\(-\frac{1}{2}\)[/tex] by [tex]\(-3y\)[/tex]:
[tex]\[
-\frac{1}{2} \cdot -3y = \frac{3}{2}y
\][/tex]
2. Multiply [tex]\(-\frac{1}{2}\)[/tex] by [tex]\(10\)[/tex]:
[tex]\[
-\frac{1}{2} \cdot 10 = -5
\][/tex]
### Step 3: Combine the results
Combine the two results to form the equivalent expression:
[tex]\[
\frac{3}{2}y - 5
\][/tex]
Therefore, the equivalent expression after combining like terms is:
[tex]\[
1.5y - 5.0
\][/tex]
