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 \((2x - 1) - 3.25(x + 3)\), we'll first simplify the original expression step by step.

1. Expand the second term:
\[
3.25(x + 3) = 3.25x + 9.75
\]

2. Substitute this back into the expression:
\[
(2x - 1) - (3.25x + 9.75)
\]

3. Distribute the negative sign:
\[
2x - 1 - 3.25x - 9.75
\]

4. Combine like terms:
- The \(x\) terms: \(2x - 3.25x = -1.25x\)
- The constant terms: \(-1 - 9.75 = -10.75\)

This gives us the simplified expression:
\[
-1.25x - 10.75
\]

Now, let's compare this result with the given responses to identify equivalent expressions.

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

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

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

4. **Expression**: \(−1.25x−10.75\)
- This is already the simplified form derived.

5. **Expression**: \(2x−1−3.25x+9.75\)
- This would result in \(2x - 3.25x - 1 + 9.75\), simplifying to \(-1.25x + 8.75\), which is not equivalent.

6. **Expression**: \(1.25x + 10.75\)
- This is not equivalent, as it has incorrect signs and different constants.

7. **Expression**: \(−1.25x−4\)
- This is not equivalent, as the constant term is incorrect.

Based on this analysis, 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 equivalent expressions are:
- \(2x−1−3.25x−9.75\)
- \(2x−3.25x−1−9.75\)
- \(−1.25x−1−9.75\)
- \(−1.25x−10.75\)