Alright, let's solve this step-by-step.
We need to add the expressions [tex]\(-6 - \frac{1}{2} p\)[/tex] and [tex]\(\frac{3}{4} p - 9\)[/tex].
Step 1: Combine like terms
1. Start with the given expressions:
[tex]\[
\left(-6 - \frac{1}{2} p\right) + \left(\frac{3}{4} p - 9\right)
\][/tex]
2. Group the constants and the terms containing [tex]\( p \)[/tex]:
[tex]\[
-6 - 9 + \left( \frac{3}{4} p - \frac{1}{2} p \right)
\][/tex]
3. Simplify the constants:
[tex]\[
-6 - 9 = -15
\][/tex]
4. Combine the coefficients of [tex]\( p \)[/tex]:
[tex]\[
\frac{3}{4} p - \frac{1}{2} p
\][/tex]
Note that [tex]\(\frac{1}{2} p\)[/tex] can be rewritten as [tex]\(\frac{2}{4} p\)[/tex], giving:
[tex]\[
\frac{3}{4} p - \frac{2}{4} p = \frac{1}{4} p
\][/tex]
5. Add the simplified constant and the simplified [tex]\( p \)[/tex] term:
[tex]\[
-15 + \frac{1}{4} p
\][/tex]
Step 2: Choose the correct multiple-choice answer
From our simplifications, we have:
[tex]\[
\frac{1}{4} p - 15
\][/tex]
Step 3: Match it with one of the provided options:
1. [tex]\(\frac{4}{8} p - 3\)[/tex] simplifies to [tex]\(\frac{1}{2} p - 3\)[/tex]
2. [tex]\(\frac{2}{6} p + (-15)\)[/tex] simplifies to [tex]\(\frac{1}{3} p - 15\)[/tex]
3. [tex]\(-\frac{2}{4} p + (-3)\)[/tex] simplifies to [tex]\(-\frac{1}{2} p - 3\)[/tex]
4. [tex]\(\frac{1}{4} p - 15\)[/tex]
We see that the correct answer matches the fourth option:
[tex]\[
\boxed{4}
\][/tex]
Thus, the answer is:
[tex]\[
4
\][/tex]
This completes the solution!
