To solve the equation [tex]\(8 - 3x = 20\)[/tex] step-by-step, let's find the correct equation for the missing step.
### Step-by-Step Solution:
1. Starting equation:
[tex]\[
8 - 3x = 20
\][/tex]
2. Isolate the term with [tex]\( x \)[/tex] by subtracting 8 from both sides:
[tex]\[
-3x = 20 - 8
\][/tex]
Simplify the right side:
[tex]\[
-3x = 12
\][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides by -3:
[tex]\[
\frac{-3x}{-3} = \frac{12}{-3}
\][/tex]
Simplify:
[tex]\[
x = -4
\][/tex]
### Missing Step Analysis:
Among the given options, the correct equation to represent the step where you divide by -3 is:
[tex]\[
-3x \cdot \left( -\frac{1}{3} \right) = 12 \cdot \left( -\frac{1}{3} \right)
\][/tex]
This represents multiplying both sides by the reciprocal of -3, which is [tex]\(-\frac{1}{3}\)[/tex], effectively dividing by -3.
So the correct selection is:
[tex]\[
-3 x \cdot\left(-\frac{1}{3}\right)=12 \cdot\left(-\frac{1}{3}\right)
\][/tex]
