Sure, let's solve the equation step-by-step to determine the value of [tex]\( x \)[/tex]:
The given equation is:
[tex]\[
6(x-4)+7=-5
\][/tex]
Step 1: Distribute the 6:
[tex]\[
6(x-4) = 6x - 24
\][/tex]
So, the equation becomes:
[tex]\[
6x - 24 + 7 = -5
\][/tex]
Step 2: Combine the constants on the left-hand side:
[tex]\[
6x - 24 + 7 = 6x - 17
\][/tex]
So, the updated equation is:
[tex]\[
6x - 17 = -5
\][/tex]
Step 3: Isolate the term with [tex]\( x \)[/tex] by adding 17 to both sides:
[tex]\[
6x - 17 + 17 = -5 + 17
\][/tex]
[tex]\[
6x = 12
\][/tex]
Step 4: Solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[
x = \frac{12}{6}
\][/tex]
[tex]\[
x = 2
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = 2
\][/tex]
Now let's match this solution with the given choices:
A. [tex]\( x = 2 \)[/tex]
B. [tex]\( x = 5 \)[/tex]
C. [tex]\( x = 4 \)[/tex]
D. [tex]\( x = 3 \)[/tex]
The correct answer is [tex]\(\boxed{A}\)[/tex], which corresponds to [tex]\( x = 2 \)[/tex].
