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Darnell was asked to use and identify appropriate properties of equality to find the value of d that makes this statement -4d – 8 = 2 + d true. He has written out his steps below. Label those steps with the property used. -4d + 4d – 8 = 2 + d + 4d (________________) -8 = 2 + 5d (combine like terms) -8 – 2 = 2 – 2 + 5d (_________________) -10 = 5d (combine like terms) -10/5 = 5d/5 (______________________) -2 = d

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Let's label Darnell's steps with the appropriate properties of equality as follows:

  1. -4d + 4d – 8 = 2 + d + 4d
    (Addition Property of Equality)

  2. -8 = 2 + 5d
    (Combine Like Terms)

  3. -8 – 2 = 2 – 2 + 5d
    (Subtraction Property of Equality)

  4. -10 = 5d
    (Combine Like Terms)

  5. -10/5 = 5d/5
    (Division Property of Equality)

  6. -2 = d
    (Final Result)

This way, each step clearly indicates which property was applied to transform the equation.