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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 given algebraic expression \((2x−1)−3.25(x+3)\), let's simplify it step by step.

  1. Distribute \(-3.25\) to both terms inside the parentheses: \[ (2x - 1) - 3.25(x + 3) = 2x - 1 - 3.25x - 9.75 \]

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

  3. Further simplify: \[ -1.25x - 1 - 9.75 = -1.25x - 10.75 \]

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

Now let's check each of the responses to see if they are equivalent to \(-1.25x - 10.75\):

  1. Response: \(2x−1−3.25x−9.75\)
    Simplifies to: \(-1.25x - 10.75\) (Equivalent)

  2. Response: \(2x−3.25x−1−9.75\)
    Simplifies to: \(-1.25x - 10.75\) (Equivalent)

  3. Response: \(-1.25x−1−9.75\)
    Simplifies to: \(-1.25x - 10.75\) (Equivalent)

  4. Response: \(-1.25x−10.75\)
    Already matches our expression. (Equivalent)

  5. Response: \(2x−1−3.25x+9.75\)
    Simplifies to: \(-1.25x + 8.75\) (Not equivalent)

  6. Response: \(1.25x+10.75\)
    Simplifies to: \(1.25x + 10.75\) (Not equivalent)

  7. Response: \(-1.25x−4\)
    Simplifies to: \(-1.25x - 4\) (Not equivalent)

Thus, the equivalent expressions are:

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