Select the THREE expressions that are equivalent to this algebraic expression.

Question

(2x−1)−3.25(x+3)


(3 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−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

Answer 1

To simplify the expression \((2x−1)−3.25(x+3)\), we can follow these steps:

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

2. Now, substitute this back into the original expression: \[ (2x - 1) - 3.25x - 9.75 \]

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

Now, we can check which of the given responses match this final expression, \(-1.25x - 10.75\):

1. 2x−1−3.25x−9.75

   • This expression simplifies to \(-1.25x - 10.75\).

2. 2x−3.25x−1−9.75

   • This also simplifies to \(-1.25x - 10.75\).

3. −1.25x−10.75

   • This is exactly equal to our expression.

4. 2x−1−3.25x+9.75

   • This simplifies to \(-1.25x + 8.75\), which does not match.

5. 1.25x + 10.75

   • This does not match as it is positive instead of negative.

6. −1.25x−4

   • This expression does not match because the constant term is incorrect.

The three equivalent expressions to \((2x−1)−3.25(x+3)\) are:

1. 2x−1−3.25x−9.75
2. 2x−3.25x−1−9.75
3. −1.25x−10.75