To find the value of the expression [tex]\((3x - 12) - \left(\frac{1}{2}xy - 10\right)\)[/tex] for [tex]\(x = 3\)[/tex] and [tex]\(y = 6\)[/tex], we will follow these steps:
1. Substitute the given values: Begin by substituting [tex]\(x = 3\)[/tex] and [tex]\(y = 6\)[/tex] into the expression.
2. Simplify the components: Compute the value of each part of the expression.
Let's break it down step by step:
### Step 1: Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the expression
The expression given is:
[tex]\[
(3x - 12) - \left( \frac{1}{2}xy - 10 \right)
\][/tex]
Substituting [tex]\(x = 3\)[/tex] and [tex]\(y = 6\)[/tex] into the expression, we get:
[tex]\[
(3 \cdot 3 - 12) - \left( \frac{1}{2} \cdot 3 \cdot 6 - 10 \right)
\][/tex]
### Step 2: Simplify the components
Simplify inside the parentheses:
[tex]\[
3 \cdot 3 = 9
\][/tex]
[tex]\[
\frac{1}{2} \cdot 3 \cdot 6 = 9
\][/tex]
Substituting these values back into the expression, we have:
[tex]\[
(9 - 12) - (9 - 10)
\][/tex]
Simplify each part:
[tex]\[
9 - 12 = -3
\][/tex]
[tex]\[
9 - 10 = -1
\][/tex]
So the expression now looks like:
[tex]\[
-3 - (-1)
\][/tex]
Simplify the overall expression:
Subtracting a negative is the same as adding the positive:
[tex]\[
-3 + 1 = -2
\][/tex]
So, the value of the expression [tex]\((3x - 12) - \left( \frac{1}{2}xy - 10 \right)\)[/tex] for [tex]\(x = 3\)[/tex] and [tex]\(y = 6\)[/tex] is:
[tex]\[
-2
\][/tex]
Therefore, the correct answer is [tex]\(-2\)[/tex].
