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

1 answer

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. \(−1.25x−10.75\)