Solve [tex]4ax + 5ax = 3ax + 6[/tex] for [tex]x[/tex]. Assume [tex]a \neq 0[/tex].

A. [tex]x = \frac{1}{a}[/tex]

B. [tex]x = a[/tex]

C. [tex]x = \frac{1}{2a}[/tex]

D. [tex]x = 2a[/tex]



Answer :

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.