Sure, let's solve the equation step-by-step and find the correct value for [tex]\( x \)[/tex].
We start with the equation:
[tex]\[ 10 = 2 - 4(a x - 3) \][/tex]
First, distribute the [tex]\(-4\)[/tex] through the parentheses:
[tex]\[ 10 = 2 - 4a x + 12 \][/tex]
Combine like terms on the right side:
[tex]\[ 10 = 14 - 4a x \][/tex]
Next, isolate the term involving [tex]\( x \)[/tex] by subtracting 14 from both sides:
[tex]\[ 10 - 14 = -4a x \][/tex]
[tex]\[ -4 = -4a x \][/tex]
Divide both sides by [tex]\(-4a\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{-4}{-4a} = x \][/tex]
[tex]\[ x = \frac{1}{a} \][/tex]
Thus, the solution to the equation [tex]\( 10 = 2 - 4(a x - 3) \)[/tex] is:
[tex]\[ x = \frac{1}{a} \][/tex]
Now, we need to select the correct answer from the given options:
A. [tex]\(\frac{5}{a}\)[/tex]
B. [tex]\(\frac{1}{a}\)[/tex]
C. [tex]\(-\frac{1}{a}\)[/tex]
D. [tex]\(-\frac{5}{a}\)[/tex]
The correct answer is:
[tex]\[ \boxed{\frac{1}{a}} \][/tex]
