Certainly! Let's solve the equation [tex]\(4ax + 5ax = 3ax + 6\)[/tex] step by step for [tex]\(x\)[/tex].
1. Combine like terms on the left-hand side and the right-hand side of the equation:
The original equation is:
[tex]\[
4ax + 5ax = 3ax + 6
\][/tex]
On the left-hand side, [tex]\(4ax + 5ax\)[/tex] can be combined to give:
[tex]\[
9ax = 3ax + 6
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the equation:
Subtract [tex]\(3ax\)[/tex] from both sides to isolate the terms involving [tex]\(x\)[/tex]:
[tex]\[
9ax - 3ax = 6
\][/tex]
Simplify the left-hand side:
[tex]\[
6ax = 6
\][/tex]
3. Isolate [tex]\(x\)[/tex] by dividing both sides by the coefficient of [tex]\(x\)[/tex]:
The coefficient of [tex]\(x\)[/tex] on the left-hand side is [tex]\(6a\)[/tex]. Divide both sides of the equation by [tex]\(6a\)[/tex]:
[tex]\[
\frac{6ax}{6a} = \frac{6}{6a}
\][/tex]
Simplify both sides:
[tex]\[
x = \frac{1}{a}
\][/tex]
Therefore, the solution to the equation [tex]\(4ax + 5ax = 3ax + 6\)[/tex] for [tex]\(x\)[/tex] is:
[tex]\[
\boxed{\frac{1}{a}}
\][/tex]
This matches choice A.
