Question

Select all of the expressions that are equivalent to this algebraic expression.

(3x−8)+(2x+5)−(4x−8)

(1 point)
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

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

x−8+5+8
x minus 8 plus 5 plus 8

x−13+8
x minus 13 plus 8

x−3+8
x minus 3 plus 8

x−21
x minus 21

x+5

Answer 1

To determine which expressions are equivalent to the original algebraic expression \((3x−8)+(2x+5)−(4x−8)\), let's simplify it step by step.

1. Start with the original expression:
\[
(3x - 8) + (2x + 5) - (4x - 8)
\]

2. Distributing the negative sign across \(-(4x - 8)\):
\[
= (3x - 8) + (2x + 5) - 4x + 8
\]

3. Combine like terms:
- Combine \(3x + 2x - 4x\):
\[
3x + 2x - 4x = x
\]
- Combine constants \(-8 + 5 + 8\):
\[
-8 + 5 + 8 = -8 + 5 + 8 = -8 + 13 = 5
\]

4. The expression simplifies to:
\[
x + 5
\]

Now, let's review the provided responses to identify which expressions are equivalent to \(x + 5\):

1. **\(3x−8+2x+5−4x−8\)**
- Equivalent (This simplifies to \(x + 5\) as worked out above).

2. **\(3x−8+2x+5−4x+8\)**
- Not Equivalent (This simplifies to \(x + 13\)).

3. **\(3x+2x−4x−8+5+8\)**
- Equivalent (This simplifies to \(x + 5\)).

4. **\(5x−4x−8+5+8\)**
- Equivalent (This simplifies to \(x + 5\)).

5. **\(x−8+5+8\)**
- Equivalent (This simplifies to \(x + 5\)).

6. **\(x−13+8\)**
- Not Equivalent (This simplifies to \(x - 5\)).

7. **\(x−3+8\)**
- Not Equivalent (This simplifies to \(x + 5\)).

8. **\(x−21\)**
- Not Equivalent (This simplifies to \(x - 21\)).

9. **\(x+5\)**
- Equivalent (This is exactly what we simplified to).

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

- \(3x−8+2x+5−4x−8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x+5\)

Thus, the equivalent expressions are:
1. \(3x−8+2x+5−4x−8\)
2. \(3x+2x−4x−8+5+8\)
3. \(5x−4x−8+5+8\)
4. \(x−8+5+8\)
5. \(x+5\)