Question

Select the THREE 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 plus 8

3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8

10x−21
10 x minus 21

x−5
x minus 5

x+5
x plus 5

x−21
x minus 21

3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8

Answer 1

To determine which of the given expressions are equivalent to the original expression \((3x - 8) + (2x + 5) - (4x - 8)\), let's simplify the expression step by step:

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

2. Distribute the negative sign across the third term:
\[
3x - 8 + 2x + 5 - 4x + 8
\]

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

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

Now, let's look through the provided responses to identify the three equivalent expressions:

1. **3x−8+2x+5−4x+8** \
Equivalent — This is just a rearrangement of the original expression.

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

3. **10x−21** \
Not equivalent — This expression does not match.

4. **x−5** \
Not equivalent — This is not equal to \(x + 5\).

5. **x+5** \
Equivalent — This is exactly the simplified result.

6. **x−21** \
Not equivalent — This does not match \(x + 5\).

7. **3x−8+2x+5−4x−8** \
Equivalent — This is the same as option 1, just rearranged.

The three equivalent expressions are:

1. \(3x - 8 + 2x + 5 - 4x + 8\)
2. \(3x + 2x - 4x - 8 + 5 + 8\)
3. \(x + 5\)

So the final answers are selections 1, 2, and 5.