Question

Select the THREE expressions that are equivalent to this algebraic expression.

(3x−8)+(2x+5)−(4x−8)

(3 points)
Responses

x−5

3x−8+2x+5−4x+8

3x+2x−4x−8+5+8

3x−8+2x+5−4x−8

x−21

10x−21

x+5

Answer 1

To simplify the algebraic expression \((3x−8)+(2x+5)−(4x−8)\), let's break it down step by step:

1. Remove the parentheses:
\[
3x - 8 + 2x + 5 - 4x + 8
\]

2. Combine like terms:
- For the \(x\) terms: \(3x + 2x - 4x = (3 + 2 - 4)x = 1x\) or simply \(x\).
- For the constant terms: \(-8 + 5 + 8 = -8 + 13 = 5\).

So, the simplified expression becomes:
\[
x + 5
\]

Now, we need to evaluate the given responses to see which three are equivalent to the original expression:

1. **\(x−5\)**: Not equivalent.
2. **\(3x−8+2x+5−4x+8\)**: Equivalent (this is just rewriting the original expression).
3. **\(3x+2x−4x−8+5+8\)**: Equivalent (this is another rearrangement of the original expression).
4. **\(3x−8+2x+5−4x−8\)**: Equivalent (again, just rewriting the original expression).
5. **\(x−21\)**: Not equivalent.
6. **\(10x−21\)**: Not equivalent.
7. **\(x+5\)**: Equivalent (this is the simplified version).

The three expressions that are equivalent to the original expression are:
- \(3x−8+2x+5−4x+8\)
- \(3x+2x−4x−8+5+8\)
- \(3x−8+2x+5−4x−8\)

In conclusion, the correct responses are:
- \(3x−8+2x+5−4x+8\)
- \(3x+2x−4x−8+5+8\)
- \(3x−8+2x+5−4x−8\) (any one of these three rewritten forms could be selected, so depending on your answer options, you can also include \(x+5\) as a final equivalent).