Question

Question
Which expressions can be added to 3x to result in the expression 5x-8? Select all that apply.
Responses

5x+8
5x+8

2x-8
2x-8

5x-8
5x-8

-8+2x
-8+2x

-2x+8

Answer 1

To determine which expressions can be added to \(3x\) to result in the expression \(5x - 8\), we need to set up an equation. We are looking for expressions \(E\) such that:

\[
3x + E = 5x - 8
\]

To find \(E\), we can rearrange the equation:

\[
E = (5x - 8) - 3x
\]
\[
E = 5x - 3x - 8
\]
\[
E = 2x - 8
\]

So, the expression that can be added to \(3x\) to result in \(5x - 8\) is \(2x - 8\).

Now, let's evaluate each of the given options:

1. **\(5x + 8\)**:
\(3x + (5x + 8) = 8x + 8\) (not equal to \(5x - 8\))

2. **\(2x - 8\)**:
\(3x + (2x - 8) = 5x - 8\) (this is a match)

3. **\(5x - 8\)**:
\(3x + (5x - 8) = 8x - 8\) (not equal to \(5x - 8\))

4. **\(-8 + 2x\)**:
\(3x + (-8 + 2x) = 5x - 8\) (this is a match since it is equivalent to \(2x - 8\))

5. **\(-2x + 8\)**:
\(3x + (-2x + 8) = x + 8\) (not equal to \(5x - 8\))

Only the following expressions can be added to \(3x\) to yield \(5x - 8\):

- \(2x - 8\)
- \(-8 + 2x\)

So the correct answers are:
- \(2x - 8\)
- \(-8 + 2x\)