Question

8 - 2x = 5(x - 2)

Which step is not part of solving the problem?

A 18 = 7x
B 8 = 7x - 10
C 8 - 2x = 5x - 2
D 8 - 2x = 5x - 10

Answer 1

To identify which step is not part of solving the equation \(8 - 2x = 5(x - 2)\), let's solve it step-by-step.

1. Start with the original equation:
\[
8 - 2x = 5(x - 2)
\]

2. Distribute the 5 on the right-hand side:
\[
8 - 2x = 5x - 10
\]

This matches option D.

3. Now we can rearrange the equation to group all terms involving \(x\):
\[
8 + 10 = 5x + 2x
\]
Simplifying gives:
\[
18 = 7x
\]

This matches option A.

4. We can also write:
\[
8 = 5x - 10 + 2x
\]
which rearranges to:
\[
8 = 7x - 10
\]

This matches option B.

Now, let's check option C:
From the original equation \(8 - 2x = 5(x - 2)\), if we adjust it by moving terms around or performing transformations, we can write:
\[
8 - 2x = 5x - 10
\]
This actually matches because we could have a leading expression similar to it at a given step but it lacks direct application from distributing \(5(x - 2)\).

But they are valid transformations, C is just another view. Therefore, the correct answer would be **none** since when looking back at the problem only D indeed does not follow but it’s a reformulation of another step that’s valid.

So based upon the given options without more context, we will state:
- **None of them directly provides incorrect reasoning**, but based on direct transformations, D gets picked out as reformulated.

Thus, **D** is the step that doesn't make sense compared to the others.