Asked by Sunshine

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

Answers

Answered by GPT-4o mini
To determine which expressions are equivalent to the expression \((2x−1)−3.25(x+3)\), we'll first simplify it step by step:

1. **Distribute** - Start by distributing \(-3.25\) across \((x + 3)\):
\[
-3.25(x + 3) = -3.25x - 3.25 \cdot 3 = -3.25x - 9.75
\]

2. **Combine the expressions** - Now substitute this back into the original expression:
\[
(2x - 1) - (3.25x + 9.75) = 2x - 1 - 3.25x - 9.75
\]

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

Now we have simplified the original expression to:
\[
-1.25x - 10.75
\]

Next, let's check which of the provided responses match \(-1.25x - 10.75\):

- **Response: `2x−1−3.25x−9.75`**: Simplifies to \(-1.25x - 10.75\) (equivalent).
- **Response: `2x−3.25x−1−9.75`**: Simplifies to \(-1.25x - 10.75\) (equivalent).
- **Response: `−1.25x−1−9.75`**: Simplifies to \(-1.25x - 10.75\) (equivalent).
- **Response: `−1.25x−10.75`**: This is exactly what we derived from the original expression (equivalent).

The other responses:
- **Response: `2x−1−3.25x+9.75`**: Would simplify to \( -1.25x + 8.75 \) (not equivalent).
- **Response: `1.25x+10.75`**: (not equivalent).
- **Response: `-1.25x−4`**: (not equivalent).

Thus, the equivalent expressions are:
1. \(2x−1−3.25x−9.75\)
2. \(2x−3.25x−1−9.75\)
3. \(-1.25x−1−9.75\)
4. \(-1.25x−10.75\)

So, the final equivalent expressions are:
- \(2x−1−3.25x−9.75\)
- \(2x−3.25x−1−9.75\)
- \(-1.25x−1−9.75\)
- \(-1.25x−10.75\)
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