Question

Select all expressions that are equivalent to this algebraic expression.

(2x−1)−3.25(x+3)

(1 point)
Responses

2x−1−3.25x−9.75
2 x minus 1 minus 3 point 2 5 x minus 9 point 7 5

2x−3.25x−1−9.75
2 x minus 3 point 2 5 x minus 1 minus 9 point 7 5

−1.25x−1−9.75
negative 1 point 2 5 x minus 1 minus 9 point 7 5

−1.25x−10.75
negative 1 point 2 5 x minus 10 point 7 5

2x−1−3.25x+9.75
2 x minus 1 minus 3 point 2 5 x plus 9 point 7 5

1.25x+10.75
1 point 2 5 x plus 10 point 7 5

−1.25x−4
negative 1 point 2 5 x minus 4
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Answer 1

To determine which expressions are equivalent to \((2x - 1) - 3.25(x + 3)\), we first simplify the original expression.

1. Distribute \(-3.25\) across \((x + 3)\):
\[
-3.25(x + 3) = -3.25x - 9.75
\]

2. Substitute back into the expression:
\[
(2x - 1) - 3.25(x + 3) = (2x - 1) - (3.25x + 9.75)
\]

3. Combine like terms:
\[
2x - 1 - 3.25x - 9.75 = (2x - 3.25x) + (-1 - 9.75) = -1.25x - 10.75
\]

Now we have simplified the expression to \(-1.25x - 10.75\).

Next, we can find which of the provided responses match \(-1.25x - 10.75\):

1. **\(2x - 1 - 3.25x - 9.75\)**
- Simplifies to \(-1.25x - 10.75\)
- **Equivalent**

2. **\(2x - 3.25x - 1 - 9.75\)**
- Simplifies to \(-1.25x - 10.75\)
- **Equivalent**

3. **\(-1.25x - 1 - 9.75\)**
- Simplifies to \(-1.25x - 10.75\)
- **Equivalent**

4. **\(-1.25x - 10.75\)**
- This is the expression we derived.
- **Equivalent**

5. **\(2x - 1 - 3.25x + 9.75\)**
- Simplifies to \(-1.25x + 8.75\) (not equivalent)

6. **\(1.25x + 10.75\)**
- This is the opposite of our expression (not equivalent)

7. **\(-1.25x - 4\)**
- Not equivalent

The equivalent expressions are:
- \(2x - 1 - 3.25x - 9.75\)
- \(2x - 3.25x - 1 - 9.75\)
- \(-1.25x - 1 - 9.75\)
- \(-1.25x - 10.75\)