To solve the equation [tex]\(6(x - 3) + 7 = -5\)[/tex], we can follow these detailed steps:
1. Expand the terms inside the parenthesis:
[tex]\[
6(x - 3) + 7 = -5
\][/tex]
Distribute the [tex]\(6\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
6x - 18 + 7 = -5
\][/tex]
2. Combine like terms on the left side of the equation:
[tex]\[
6x - 11 = -5
\][/tex]
3. Isolate the variable term:
Add 11 to both sides of the equation to get:
[tex]\[
6x - 11 + 11 = -5 + 11
\][/tex]
Simplifying, we get:
[tex]\[
6x = 6
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 6:
[tex]\[
\frac{6x}{6} = \frac{6}{6}
\][/tex]
Simplifying, we find:
[tex]\[
x = 1
\][/tex]
Thus, the solution to the equation [tex]\(6(x - 3) + 7 = -5\)[/tex] is [tex]\(x = 1\)[/tex].
The correct answer is:
D. [tex]\(x = 1\)[/tex]
