Question

Steps for solving 5(2x - 8) = 20 are shown.
Which of these is not part of the solution process?
5(2x - 8) = 20
102-40=20
10x - 40 + 40 = 20 + 40 Step 2
10z = 60
102
60
10
£=6
Original Equation
Step 1
Step3
Step 4
Step 5
Using the commutative property
Combining like terms
Dividing both sides by 10 to isolate the variable
Using the distributive property

Answer 1

Let's go through the steps provided to identify which one does not belong in the solution process for the equation \(5(2x - 8) = 20\).

1. **Original Equation**: \(5(2x - 8) = 20\)

2. **Step 1**: This step appears to be using the distributive property. Distributing \(5\) across \((2x - 8)\):
\[
5 \cdot 2x - 5 \cdot 8 = 10x - 40
\]
So, the equation becomes \(10x - 40 = 20\).

3. **Step 2**: The transition you wrote down seems incorrect ("102 - 40 = 20"), as \(10x - 40 = 20\) would lead to the next step being:
\[
10x - 40 + 40 = 20 + 40
\]
This is valid, as it adds \(40\) to both sides of the equation.

4. **Step 3**: The equation now becomes \(10x = 60\).

5. **Step 4**: This is dividing both sides by \(10\):
\[
\frac{10x}{10} = \frac{60}{10} \Rightarrow x = 6
\]

6. **Step 5**: You provided “Using the commutative property”, but the commutative property is not used in solving this equation. Instead, this process involves using the distributive property (for \(5(2x - 8)\)), and then combining like terms and solving for \(x\) through addition and division.

In conclusion, the step that is **not part of the solution process** is **"Using the commutative property."**