Let's solve the given equation step by step:
[tex]\[
9x - 4(x - 2) = x + 20
\][/tex]
First, distribute the [tex]\(-4\)[/tex] on the left-hand side:
[tex]\[
9x - 4x + 8 = x + 20
\][/tex]
This simplifies to:
[tex]\[
5x + 8 = x + 20
\][/tex]
Next, we want to isolate [tex]\(x\)[/tex] on one side of the equation. To do this, subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
5x - x + 8 = 20
\][/tex]
[tex]\[
4x + 8 = 20
\][/tex]
Now, subtract [tex]\(8\)[/tex] from both sides:
[tex]\[
4x + 8 - 8 = 20 - 8
\][/tex]
[tex]\[
4x = 12
\][/tex]
Finally, divide both sides by [tex]\(4\)[/tex]:
[tex]\[
x = \frac{12}{4}
\][/tex]
[tex]\[
x = 3
\][/tex]
So, the solution to the equation is [tex]\(x = 3\)[/tex]. Therefore, the correct answer is [tex]\( \boxed{A} \)[/tex].
