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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

1 answer

To determine which expressions are equivalent to the expression \((2x−1)−3.25(x+3)\), we'll first simplify it step by step:

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

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

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

Now we have simplified the original expression to: \[ -1.25x - 10.75 \]

Next, let's check which of the provided responses match \(-1.25x - 10.75\):

  • Response: 2x−1−3.25x−9.75: Simplifies to \(-1.25x - 10.75\) (equivalent).
  • Response: 2x−3.25x−1−9.75: Simplifies to \(-1.25x - 10.75\) (equivalent).
  • Response: −1.25x−1−9.75: Simplifies to \(-1.25x - 10.75\) (equivalent).
  • Response: −1.25x−10.75: This is exactly what we derived from the original expression (equivalent).

The other responses:

  • Response: 2x−1−3.25x+9.75: Would simplify to \( -1.25x + 8.75 \) (not equivalent).
  • Response: 1.25x+10.75: (not equivalent).
  • Response: -1.25x−4: (not equivalent).

Thus, the equivalent expressions are:

  1. \(2x−1−3.25x−9.75\)
  2. \(2x−3.25x−1−9.75\)
  3. \(-1.25x−1−9.75\)
  4. \(-1.25x−10.75\)

So, the final equivalent expressions are:

  • \(2x−1−3.25x−9.75\)
  • \(2x−3.25x−1−9.75\)
  • \(-1.25x−1−9.75\)
  • \(-1.25x−10.75\)