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 the equivalent expressions to \((2x−1)−3.25(x+3)\), let's simplify it step by step:

1. Start with the original expression:
\[
(2x - 1) - 3.25(x + 3)
\]

2. Distribute \(-3.25\) into \((x + 3)\):
\[
(2x - 1) - (3.25x + 9.75)
\]

3. Now rewrite the expression:
\[
2x - 1 - 3.25x - 9.75
\]

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

Now we can compare this result \(-1.25x - 10.75\) with the given options:

1. **\(2x−1−3.25x−9.75\)** → This simplifies to \(-1.25x - 10.75\) (True)
2. **\(2x−3.25x−1−9.75\)** → This also simplifies to \(-1.25x - 10.75\) (True)
3. **\(-1.25x−1−9.75\)** → This simplifies to \(-1.25x - 10.75\) (True)
4. **\(-1.25x−10.75\)** → This expression is equivalent to our final result (True)
5. **\(2x−1−3.25x+9.75\)** → This becomes \(2x - 3.25x + 8.75\) → \(-1.25x + 8.75\) (Not equal)
6. **\(1.25x + 10.75\)** → This is not equivalent to our expression (Not equal)
7. **\(-1.25x−4\)** → This is not equivalent to our expression (Not equal)

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