Question

a b c or d
Select all of the expressions that are equivalent to this algebraic expression.

(3x−8)+(2x+5)−(4x−8)


(3 points)
Responses

3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8

3x−8+2x+5−4x+8
3 x minus 8 plus 2 x plus 5 minus 4 x plus 8

3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8

x−13+8
x minus 13 plus 8

x−21
x minus 21

x+5

Answer 1

To determine which expressions are equivalent to the original expression \((3x−8)+(2x+5)−(4x−8)\), we need to simplify the original expression first.

1. **Distributing and combining like terms**:
- Start with \((3x - 8) + (2x + 5) - (4x - 8)\).
- This can be rewritten as:
\[
3x - 8 + 2x + 5 - 4x + 8
\]
- Now, combine like terms:
- \(3x + 2x - 4x = (3 + 2 - 4)x = 1x = x\)
- \(-8 + 5 + 8 = -8 + 13 = 5\)

So, simplifying gives:
\[
x + 5
\]

Now, let's analyze the responses:

1. **\(3x−8+2x+5−4x−8\)**: This is equivalent (it's just a rearrangement of the original expression).

2. **\(3x−8+2x+5−4x+8\)**: This is not equivalent because it changes \(-8\) to \(+8\) (which alters the constant term).

3. **\(3x+2x−4x−8+5+8\)**: This is equivalent after simplification (same terms as above).

4. **\(x−13+8\)**: This is not equivalent since it simplifies to \(x - 5\), not \(x + 5\).

5. **\(x−21\)**: This is not equivalent as it is different from \(x + 5\).

6. **\(x+5\)**: This is equivalent.

Based on this analysis, the equivalent expressions are:
- \(3x−8+2x+5−4x−8\)
- \(3x+2x−4x−8+5+8\)
- \(x+5\)

Thus, the selected responses are:
- **a** (3x−8+2x+5−4x−8)
- **c** (3x+2x−4x−8+5+8)
- **g** (x+5)