To solve the equation [tex]\( -5(x - 20) = 35 \)[/tex], let's go through the steps in detail:
1. Distribute the [tex]\(-5\)[/tex] on the left side:
[tex]\[
-5(x - 20) = -5x + 100
\][/tex]
2. Set the left side equal to the right side:
[tex]\[
-5x + 100 = 35
\][/tex]
3. Combine like terms:
This step is done to isolate the term involving [tex]\(x\)[/tex]. To do this, subtract 100 from both sides of the equation to move the constant term to the right side.
[tex]\[
-5x + 100 - 100 = 35 - 100
\][/tex]
Simplifying this, we get:
[tex]\[
-5x = -65
\][/tex]
4. Divide both sides of the equation by [tex]\(-5\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-65}{-5}
\][/tex]
Performing this division:
[tex]\[
x = 13
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that makes the equation true is [tex]\(13\)[/tex].
The correct answer is [tex]\( \boxed{13} \)[/tex].
