Question

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Question
Select all expressions that are equivalent to this algebraic expression.

(2x−1)−3.25(x+3)


(4 points)
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

Answer 1

To determine which expressions are equivalent to the algebraic expression \((2x−1)−3.25(x+3)\), we can simplify the original expression step by step:

1. Distribute \(-3.25\) to the terms inside the parentheses:
\[
-3.25(x + 3) = -3.25x - 9.75
\]

2. Now combine the distributed terms with the rest of the expression:
\[
(2x - 1) - 3.25x - 9.75
\]

3. Combine like terms (the \(2x\) and \(-3.25x\)):
\[
2x - 3.25x = -1.25x
\]

4. Combine the constant terms (\(-1\) and \(-9.75\)):
\[
-1 - 9.75 = -10.75
\]

Thus, the simplified expression is:
\[
-1.25x - 10.75
\]

Now let's evaluate the options:

1. **\(2x−1−3.25x−9.75\)**: This simplifies to \(-1.25x - 10.75\), which is equivalent.
2. **\(2x−3.25x−1−9.75\)**: This also simplifies to \(-1.25x - 10.75\), so it is equivalent.
3. **\(-1.25x−1−9.75\)**: This simplifies to \(-1.25x - 10.75\), which is equivalent.
4. **\(-1.25x−10.75\)**: This is identical to our result, so it is equivalent.
5. **\(2x−1−3.25x+9.75\)**: This results in \(-1.25x + 8.75\), which is not equivalent.
6. **\(1.25x+10.75\)**: This has the opposite sign for both terms, so it is not equivalent.
7. **\(-1.25x−4\)**: This has a different constant term, so it is not equivalent.

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

So, the correct responses are the first four options.