9514 1404 393
Answer:
(c) identity property of addition
Step-by-step explanation:
The distributive property is used to get to step 2.
The addition property is used to get to steps 4 and 5.
The division property is used to get to the last step.
The identity property of addition is not explicitly used.
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Additional comment
Actually, the identity property of addition is used wherever the addition property is used to eliminate a term. For example, when we add 10p to get to step 4, we have actually done this:
-p +22 = -10p -14 . . . . . step 3
-p +10p +22 = -10p +10p -14 . . . . . add 10p to both sides (addition property of equality)
9p +22 = 0p -14 . . . . . . collect terms
9p +22 = 0 -14 . . . . . . . zero product rule (the product is 0 when a factor is 0)
9p +22 = -14 . . . . . . . . . identity property of addition (anything added to zero is itself)
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Similarly, the identity property of multiplication is used whenever the multiplication or division property is used to eliminate a coefficient:
9p/9 = -36/9 . . . . division property of equality
1p = -4 . . . . . . . . . .carry out the division
p = -4 . . . . . . . . . . identity property of multiplication (anything multiplied by 1 is itself)
