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
x plus 5
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Answer 1

To determine which expressions are equivalent to the original expression \((3x−8)+(2x+5)−(4x−8)\), we can simplify the original expression step-by-step:

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

2. **Combine like terms:**
\[
(3x + 2x - 4x) + (-8 + 5 + 8) = (3 + 2 - 4)x + (-8 + 5 + 8)
\]
\[
= 1x + 5 = x + 5
\]

Now that we have simplified the original expression to \(x + 5\), let’s evaluate the provided responses:

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

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

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

4. **5x−4x−8+5+8**
This simplifies to \(x + 5\) (as shown above). **Equivalent**

5. **x−8+5+8**
This simplifies to \(x + 5\) (as shown above). **Equivalent**

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

7. **x−3+8**
This simplifies to \(x + 5\). **Equivalent**

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

9. **x+5**
This is directly equivalent to \(x + 5\). **Equivalent**

Based on this analysis, the equivalent expressions 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

Choose all expressions that are equivalent from the options provided.