To evalueate this, first we replace all the veriables for the given numbers:
[tex]\frac{1}{2}(10p-7q)\longrightarrow\begin{cases}p=9 \\ q=2\end{cases}\Longrightarrow\frac{1}{2}(10\cdot9-7\cdot2)[/tex]
Now, we will follow the order of operations. We start by the parts inside parenthesis. There, we have multiplications and a substraction. Multiplications are done first, so:
[tex]\frac{1}{2}(10\cdot9-7\cdot2)=\frac{1}{2}(90-14)[/tex]
Now, we finish the operations in the parenthesis:
[tex]\frac{1}{2}(90-14)=\frac{1}{2}(76)[/tex]
The number 76 is the same as 76/1, so we can do fraction multiplication:
[tex]\frac{1}{2}(76)=\frac{1}{2}\cdot\frac{76}{1}=\frac{1\cdot76}{2\cdot1}=\frac{76}{2}=38[/tex]
So, the result is 38.
