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a b c or d 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
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

1 answer

To determine which expressions are equivalent to the original expression \( (2x - 1) - 3.25(x + 3) \), we first need to simplify the original expression.

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

  2. Rewrite it: \[ 2x - 1 - 3.25x - 9.75 \]

  3. Combine like terms:

    • Combine the \(x\) terms: \(2x - 3.25x = -1.25x\)
    • Combine the constant terms: \(-1 - 9.75 = -10.75\)

So the simplified form of the expression is: \[ -1.25x - 10.75 \]

Now, let's evaluate the proposed responses:

  1. \(2x - 1 - 3.25x - 9.75\): Simplifies to \(-1.25x - 10.75\) → This expression is equivalent.

  2. \(2x - 3.25x - 1 - 9.75\): Also simplifies to \(-1.25x - 10.75\) → This expression is equivalent.

  3. \(-1.25x - 1 - 9.75\): Combines to \(-1.25x - 10.75\) → This expression is equivalent.

  4. \(-1.25x - 10.75\): This is the exact equivalent of our original simplified expression → This expression is equivalent.

  5. \(2x - 1 - 3.25x + 9.75\): The constant combines to \(-1 + 9.75 = 8.75\), so we get \(-1.25x + 8.75\), which is not equivalent.

  6. \(1.25x + 10.75\): This is unrelated to our expression → This expression is not equivalent.

  7. \(-1.25x - 4\): This is not equivalent to \(-1.25x - 10.75\) → This expression is not equivalent.

Thus, the equivalent expressions are:

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