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 of the given expressions are equivalent to the original expression \((3x−8)+(2x+5)−(4x−8)\), we will simplify the original expression step by step.

1. **Distribute the negative sign** in \(-(4x - 8)\):
\[
(3x - 8) + (2x + 5) - 4x + 8
\]

2. **Combine like terms**:
- \(3x + 2x - 4x\)
- Combine the constants: \(-8 + 5 + 8\)

Simplifying \(3x + 2x - 4x\):
\[
3x + 2x - 4x = 5x - 4x = x
\]

Simplifying the constants:
\[
-8 + 5 + 8 = -8 + 13 = 5
\]

So, the expression simplifies to:
\[
x + 5
\]

Now, let's check which of the given options are equivalent to \(x + 5\):

1. **Option 1**: \(3x−8+2x+5−4x−8\)
- This simplifies to \(x + 5\) (True)

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

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

4. **Option 4**: \(5x−4x−8+5+8\)
- This simplifies to \(x + 5\) (True)

5. **Option 5**: \(x−8+5+8\)
- This simplifies to \(x + 5\) (True)

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

7. **Option 7**: \(x−3+8\)
- This simplifies to \(x + 5\) (True)

8. **Option 8**: \(x−21\)
- This is not equivalent (Not equivalent)

9. **Option 9**: \(x+5\)
- This is equivalent (True)

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

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

### Final List of Equivalent Expressions:
- \(3x−8+2x+5−4x−8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x−3+8\)
- \(x+5\)