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

2x−3.25x−1−9.75


−1.25x−1−9.75


−1.25x−10.75


2x−1−3.25x+9.75

1.25x+10.75

−1.25x−4

Answer 1

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

Starting with:

\[
(2x−1)−3.25(x+3)
\]

Distribute the \(-3.25\) across \((x + 3)\):

\[
(2x - 1) - (3.25x + 9.75)
\]

Now combine like terms:

\[
2x - 1 - 3.25x - 9.75
\]

Combine the \(x\) terms and the constant terms:

\[
(2x - 3.25x) + (-1 - 9.75)
\]

This simplifies to:

\[
-1.25x - 10.75
\]

Now, we need to check which of the provided options are equivalent to \(-1.25x - 10.75\):

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

2. **\(2x−3.25x−1−9.75\)**: This also simplifies to \(-1.25x - 10.75\). **(Equivalent)**

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

4. **\(−1.25x−10.75\)**: This is exactly the same as \(-1.25x - 10.75\). **(Equivalent)**

5. **\(2x−1−3.25x+9.75\)**: This simplifies to \(-1.25x + 8.75\). **(Not Equivalent)**

6. **\(1.25x + 10.75\)**: This is \(1.25x + 10.75\). **(Not Equivalent)**

7. **\(−1.25x−4\)**: This simplifies to \(-1.25x - 4\). **(Not Equivalent)**

So, the equivalent expressions are:

- \(2x−1−3.25x−9.75\)
- \(2x−3.25x−1−9.75\)
- \(−1.25x−1−9.75\)
- \(−1.25x−10.75\)

Thus, the correct responses are:

1. \(2x−1−3.25x−9.75\)
2. \(2x−3.25x−1−9.75\)
3. \(−1.25x−1−9.75\)
4. \(−1.25x−10.75\)