To solve the algebraic expression:
[tex]\[ -6(2x - 9) + (7 - 6x) \][/tex]
we need to follow these steps:
### Step 1: Distribute [tex]\(-6\)[/tex] in the first term
[tex]\[ -6 \cdot (2x) - 6 \cdot (-9) \][/tex]
This simplifies to:
[tex]\[ -12x + 54 \][/tex]
So the expression becomes:
[tex]\[ -12x + 54 + 7 - 6x \][/tex]
### Step 2: Combine like terms
We combine the [tex]\(x\)[/tex] terms and the constant terms separately.
For the [tex]\(x\)[/tex] terms:
[tex]\[ -12x - 6x = -18x \][/tex]
For the constants:
[tex]\[ 54 + 7 = 61 \][/tex]
### Step 3: Write the simplified expression
By combining the terms, we have:
[tex]\[ -18x + 61 \][/tex]
### Step 4: Match the simplified expression with one of the given choices
Looking at the provided choices:
- [tex]\( \text{E.} \quad -18x + 47 \)[/tex]
- [tex]\( \text{F.} \quad -18x + 61 \)[/tex]
- [tex]\( \text{G.} \quad -6x + 47 \)[/tex]
- [tex]\( \text{H.} \quad -6x + 61 \)[/tex]
The simplified expression [tex]\(-18x + 61\)[/tex] matches choice [tex]\(F\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{F} \][/tex]
