Can somebody me on this question, i really need an answer. what are the reasons for a, b,c, and, d?

Short Answers (Explanation in next section below)

Reason A: Distributive Property

Reason B: Additive Property of Equality

Reason C: Combine like terms

Reason D: Additive Identity Property



Further Explanation:

Reason A: The distributive property is the idea where we multiply a number by a block of values inside a parenthesis. In this case we have 3 outside the parenthesis multiplied by the x inside and the -4 inside as well. So 3 times x = 3x and 3 times -4 = -12 indicating that 3*(x-4) = 3*x+3*(-4) = 3x-12. Be sure to multiply the outer 3 by EVERY term inside the parenthesis. Often it is easy to forget a term inside.

Reason B: We are adding 12 to both sides. The goal is to have the -12 go away. Notice in the next line -12+12 = 0 which is effectively canceled out. Adding the same value to both sides is the Additive Property of Equality. It must be done to both sides to balance things out. The general rule is that if a = b, then a+c = b+c. We have added c to both sides.

Reason C: We just do arithmetic here. On the left side -12+12 turns into 0. On the right side 33+12 turns into 45. This is considered "combine like terms" as all of these terms have something in common: they don't have variables attached to them. Which is why they are common or like terms

Reason D: The additive identity property says that adding 0 to anything leads to the same thing as before. For example, adding zero to 5 gets us 5+0 = 5. Nothing has changed, which is what we expect. That's why 3x+0 turns into 3x. At this point, the -12 a few steps prior has been canceled out. In general, the additive identity property is x+0 = x or 0+x = x