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

a b c or d

Answer 2

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

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

2. Combine like terms:
- For the \(x\) terms: \(3x + 2x - 4x = 1x\) or simply \(x\).
- For the constant terms: \(-8 + 5 + 8 = -8 + 5 + 8 = -8 + 13 = 5\).

So, the simplified expression is:
\[
x + 5
\]

Now we can check each of the provided responses to see if they simplify to \(x + 5\).

1. **3x−8+2x+5−4x−8**
- This simplifies to \(3x + 2x - 4x - 8 + 5 - 8 = x - 8 + 5 = x - 3\), which is not equivalent.

2. **3x−8+2x+5−4x+8**
- This simplifies to \(3x + 2x - 4x - 8 + 5 + 8 = x + 5\), which is equivalent.

3. **3x+2x−4x−8+5+8**
- This also simplifies to \(3x + 2x - 4x - 8 + 5 + 8 = x + 5\), which is equivalent.

4. **5x−4x−8+5+8**
- This simplifies to \(x - 8 + 5 + 8 = x + 5\), which is equivalent.

5. **x−8+5+8**
- This simplifies to \(x - 8 + 5 + 8 = x + 5\), which is equivalent.

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

7. **x−3+8**
- This simplifies to \(x + 5\), which is equivalent.

8. **x−21**
- This is just \(x - 21\), which is not equivalent.

9. **x+5**
- This is the expression itself, so it is equivalent.

Based on this evaluation, 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**

So the final equivalent expressions selected are:
- \(3x−8+2x+5−4x+8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x−3+8\)
- \(x+5\)

Answer 3

Based on the evaluation of the expressions provided, the equivalent options are:

- **b) 3x−8 + 2x + 5 − 4x + 8**
- **c) 3x + 2x − 4x − 8 + 5 + 8**
- **d) 5x − 4x − 8 + 5 + 8**
- **e) x − 8 + 5 + 8**
- **g) x − 3 + 8**
- **h) x + 5**

If I were to narrow it down to just options a, b, c, or d, the correct answers would be:

- **b) 3x−8+2x+5−4x+8**
- **c) 3x+2x−4x−8+5+8**
- **d) 5x−4x−8+5+8**

Thus, the correct options are **b**, **c**, and **d**.