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

Answer 1

To determine which expressions are equivalent to the given algebraic expression \((2x−1)−3.25(x+3)\), let's simplify it step by step.

1. Distribute \(-3.25\) to both terms inside the parentheses:
\[
(2x - 1) - 3.25(x + 3) = 2x - 1 - 3.25x - 9.75
\]

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

3. Further simplify:
\[
-1.25x - 1 - 9.75 = -1.25x - 10.75
\]

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

Now let's check each of the responses to see if they are equivalent to \(-1.25x - 10.75\):

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

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

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

4. **Response:** \(-1.25x−10.75\)
**Already matches our expression.** (Equivalent)

5. **Response:** \(2x−1−3.25x+9.75\)
**Simplifies to:** \(-1.25x + 8.75\) (Not equivalent)

6. **Response:** \(1.25x+10.75\)
**Simplifies to:** \(1.25x + 10.75\) (Not equivalent)

7. **Response:** \(-1.25x−4\)
**Simplifies to:** \(-1.25x - 4\) (Not equivalent)

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