To find the value of the expression [tex]\((2x - 12) + \left(\frac{1}{2}xy - 10\right)\)[/tex] for [tex]\(x = 4\)[/tex] and [tex]\(y = 7\)[/tex], we can follow these steps:
1. Calculate the first part of the expression:
[tex]\[
2x - 12
\][/tex]
Substitute [tex]\(x = 4\)[/tex] into the expression:
[tex]\[
2(4) - 12 = 8 - 12 = -4
\][/tex]
2. Calculate the second part of the expression:
[tex]\[
\frac{1}{2}xy - 10
\][/tex]
Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 7\)[/tex] into the expression:
[tex]\[
\frac{1}{2}(4)(7) - 10 = \frac{1}{2}(28) - 10 = 14 - 10 = 4
\][/tex]
3. Add the results of the two parts together:
[tex]\[
(2x - 12) + \left(\frac{1}{2}xy - 10\right) = -4 + 4 = 0
\][/tex]
Therefore, the value of the expression for [tex]\(x = 4\)[/tex] and [tex]\(y = 7\)[/tex] is:
[tex]\[
\boxed{0}
\][/tex]
