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Question
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
x plus 5
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page 12 of 12
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Answer 1

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

1. **Distribute and combine like terms**:
\[
(3x - 8) + (2x + 5) - (4x - 8)
\]
This can be written as:
\[
3x - 8 + 2x + 5 - 4x + 8
\]

2. **Combine the x terms**:
\[
(3x + 2x - 4x) + (-8 + 5 + 8)
\]
Simplifying the x terms:
\[
3x + 2x - 4x = x
\]
And simplifying the constant terms:
\[
-8 + 5 + 8 = -8 + 5 + 8 = 5
\]

3. **Final simplified expression**:
The entire expression simplifies to:
\[
x + 5
\]

Now we can evaluate the given options to see which are equivalent to \(x + 5\).

**Responses**:
1. \(3x - 8 + 2x + 5 - 4x - 8\) (This is equivalent since we simplified it to \(x + 5\).)

2. \(3x - 8 + 2x + 5 - 4x + 8\) (This simplifies to \(3x + 2x - 4x - 8 + 5 + 8 = x + 5\).)

3. \(3x + 2x - 4x - 8 + 5 + 8\) (This also simplifies to \(x + 5\).)

4. \(x - 13 + 8\) (This simplifies to \(x - 5\), which is **not equivalent**.)

5. \(x - 21\) (This is clearly **not equivalent**.)

6. \(x + 5\) (This is clearly equivalent as it is exactly \(x + 5\).)

**Conclusion**:
The expressions that are equivalent to \( (3x−8)+(2x+5)−(4x−8) \) are:
- \(3x - 8 + 2x + 5 - 4x - 8\)
- \(3x - 8 + 2x + 5 - 4x + 8\)
- \(3x + 2x - 4x - 8 + 5 + 8\)
- \(x + 5\)