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. \(-1.25x - 10.75\)