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

(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
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1 answer

To solve the expression \((2x−1)−3.25(x+3)\), let's distribute and simplify it step by step:

  1. Distribute \(-3.25\) to both terms inside the parentheses: \[ -3.25(x + 3) = -3.25x - 3.25 \times 3 = -3.25x - 9.75 \]

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

  3. Simplify by combining like terms:

    • Combine \(2x\) and \(-3.25x\): \[ 2x - 3.25x = -1.25x \]
    • Combine \(-1\) and \(-9.75\): \[ -1 - 9.75 = -10.75 \]

  4. Putting it all together, we have: \[ -1.25x - 10.75 \]

Now, let's compare this result with the provided options to find the three equivalent expressions:

  1. \(2x - 1 - 3.25x - 9.75\) simplifies to \(-1.25x - 10.75\) (equivalent).
  2. \(2x - 3.25x - 1 - 9.75\) also simplifies to \(-1.25x - 10.75\) (equivalent).
  3. \(-1.25x - 10.75\) is exactly our simplified expression (equivalent).
  4. \(2x - 1 - 3.25x + 9.75\) simplifies to \(2x - 3.25x + 8.75\), which is \(-1.25x + 8.75\) (not equivalent).
  5. \(1.25x + 10.75\) does not match (\( -1.25x - 10.75\)).
  6. \(-1.25x - 4\) does not match either (\(-10.75\) is different from \(-4\)).

Thus, the three equivalent expressions are:

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