To find the value of the expression [tex]\((4x - 12) + \left(\frac{1}{2}xy - 10\right)\)[/tex] for [tex]\(x = 4\)[/tex] and [tex]\(y = 6\)[/tex], let's break down the problem into two main parts and solve each part step by step.
1. Calculate [tex]\(4x - 12\)[/tex]:
a. Substitute [tex]\(x = 4\)[/tex] into the expression [tex]\(4x - 12\)[/tex].
[tex]\(4 \cdot 4 - 12 = 16 - 12 = 4\)[/tex]
So, the value of the first part is [tex]\(4\)[/tex].
2. Calculate [tex]\(\frac{1}{2}xy - 10\)[/tex]:
a. Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 6\)[/tex] into the expression [tex]\(\frac{1}{2}xy - 10\)[/tex].
[tex]\(\frac{1}{2} \cdot 4 \cdot 6 = \frac{1}{2} \cdot 24 = 12\)[/tex]
b. Subtract [tex]\(10\)[/tex] from [tex]\(12\)[/tex].
[tex]\(12 - 10 = 2\)[/tex]
So, the value of the second part is [tex]\(2\)[/tex].
3. Add the results from the two parts:
The value of [tex]\((4x - 12) + \left(\frac{1}{2}xy - 10\right)\)[/tex] is given by:
[tex]\(4 + 2 = 6\)[/tex]
Hence, the value of the expression [tex]\((4x - 12) + \left(\frac{1}{2}xy - 10\right)\)[/tex] for [tex]\(x = 4\)[/tex] and [tex]\(y = 6\)[/tex] is [tex]\(6\)[/tex].
