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 need to perform the calculations step-by-step as follows:
1. Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 6\)[/tex] into the expression.
2. First, calculate the inner expressions:
[tex]\[
3x - 12 = 3(3) - 12 = 9 - 12 = -3
\][/tex]
[tex]\[
\frac{1}{2}xy - 10 = \frac{1}{2}(3)(6) - 10 = \frac{1}{2}(18) - 10 = 9 - 10 = -1
\][/tex]
3. Now substitute these results into the overall expression:
[tex]\[
(3x - 12) - \left(\frac{1}{2}xy - 10\right) = -3 - (-1)
\][/tex]
4. Simplify the expression:
[tex]\[
-3 - (-1) = -3 + 1 = -2
\][/tex]
So, the value of the expression is [tex]\(-2\)[/tex].
Therefore, the correct answer is [tex]\(-2\)[/tex].
