To simplify the given expression:
[tex]\[
\left(-\frac{11}{2} x + 3\right) - 2\left(-\frac{11}{4} x - \frac{5}{2}\right)
\][/tex]
First, distribute the -2 within the parentheses:
[tex]\[
-2 \left(-\frac{11}{4} x - \frac{5}{2}\right) = -2 \cdot \left(-\frac{11}{4} x\right) - 2 \cdot \left(-\frac{5}{2}\right)
\][/tex]
Distribute the -2 to each term:
[tex]\[
-2 \left(-\frac{11}{4} x\right) = \frac{22}{4} x = \frac{11}{2} x
\][/tex]
[tex]\[
-2 \left(-\frac{5}{2}\right) = 5
\][/tex]
So, the expression simplifies to:
[tex]\[
\left(-\frac{11}{2} x + 3\right) + \left(\frac{11}{2} x + 5\right)
\][/tex]
Now combine the like terms:
[tex]\[
-\frac{11}{2} x + \frac{11}{2} x + 3 + 5
\][/tex]
The [tex]\(\frac{11}{2} x\)[/tex] terms cancel each other out:
[tex]\[
0x + 3 + 5 = 8
\][/tex]
Therefore, the simplified form of the expression is:
[tex]\[
8
\][/tex]
