Question

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 Skip to navigation

Answer 1

To determine which expressions are equivalent to \((2x - 1) - 3.25(x + 3)\), we will simplify the original expression and then compare it with the given responses.

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

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

3. Combine like terms:
\[
2x - 3.25x - 1 - 9.75 = -1.25x - 10.75
\]

Now we have simplified \((2x - 1) - 3.25(x + 3)\) to \(-1.25x - 10.75\).

Next, we need to check each option to see if it is 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 simplifies to \(-1.25x - 10.75\). (Equivalent)

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

4. **\(-1.25x - 10.75\)**
- Already in the simplified form. (Equivalent)

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

6. **\(1.25x + 10.75\)**
- This is not equivalent. (Not Equivalent)

7. **\(-1.25x - 4\)**
- This is not equivalent. (Not Equivalent)

The only equivalent expressions from the selections provided 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 answers are:
1. \(2x - 1 - 3.25x - 9.75\)
2. \(2x - 3.25x - 1 - 9.75\)
3. \(-1.25x - 1 - 9.75\)
4. \(-1.25x - 10.75\)