To solve the equation [tex]\(5ax + 3ax = 4ax + 12\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Combine Like Terms on the Left Side:
The left side of the equation has two terms that both contain [tex]\(ax\)[/tex]. Combine these terms:
[tex]\[5ax + 3ax = (5 + 3)ax = 8ax\][/tex]
So the equation now simplifies to:
[tex]\[8ax = 4ax + 12\][/tex]
2. Move All [tex]\(ax\)[/tex] Terms to One Side:
Subtract [tex]\(4ax\)[/tex] from both sides of the equation to get all the [tex]\(ax\)[/tex] terms on one side:
[tex]\[8ax - 4ax = 12\][/tex]
Simplify the left side:
[tex]\[4ax = 12\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides of the equation by [tex]\(4a\)[/tex]. Remember, [tex]\(a \neq 0\)[/tex]:
[tex]\[\frac{4ax}{4a} = \frac{12}{4a}\][/tex]
Simplify the fractions:
[tex]\[x = \frac{12}{4a} = \frac{3}{a}\][/tex]
Therefore, the solution for [tex]\(x\)[/tex] is:
[tex]\[x = \frac{3}{a}\][/tex]
So, the correct answer is:
[tex]\[ \boxed{x = \frac{3}{a}} \][/tex]
This matches choice C.
