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Which expressions are equivalent to 5 x minus 15? Select three options.

5 (x + 15)
5 (x minus 3)
4 x + 3 y minus 15 minus 3 y + x
Negative 7 y minus 6 x minus 8 y + x
Negative 20 minus 3 x + 5 + 8 x

1 answer

To find expressions equivalent to \(5x - 15\), we can simplify each option. Let's analyze them one by one:

  1. \(5 (x + 15)\): \[ 5(x + 15) = 5x + 75 \quad (\text{not equivalent}) \]

  2. \(5 (x - 3)\): \[ 5(x - 3) = 5x - 15 \quad (\text{equivalent}) \]

  3. \(4x + 3y - 15 - 3y + x\): Simplifying the expression: \[ 4x + 3y - 3y - 15 + x = 4x + x - 15 = 5x - 15 \quad (\text{equivalent}) \]

  4. \(-7y - 6x - 8y + x\): Simplifying this expression: \[ -7y - 8y - 6x + x = -15y - 5x \quad (\text{not equivalent}) \]

  5. \(-20 - 3x + 5 + 8x\): Simplifying this expression: \[ -20 + 5 + 8x - 3x = -15 + 5x \quad (\text{not equivalent}) \]

The equivalent expressions to \(5x - 15\) are:

  • \(5(x - 3)\)
  • \(4x + 3y - 15 - 3y + x\)

So the three options that are equivalent to \(5x - 15\) are:

  1. \(5 (x - 3)\)
  2. \(4x + 3y - 15 - 3y + x\)

Since we only found two so far, I must clarify that we only found two expressions from the provided list. Please check if there are more options or if any were mislisted. The correct answers are:

  • \(5 (x - 3)\)
  • \(4x + 3y - 15 - 3y + x\)