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23 votes
23 votes
-2(4p - 11) + 7p = -10p - 14

-8p + 22 + 7p = -10p - 14
-p + 22 = -10p - 14
9p + 22 = -14
9p = -39
p = -4
Which property is not needed to justify any of the steps?
division property of equality
identity property of addition
addition property of equality

-2(4p - 11) + 7p = -10p - 14 -8p + 22 + 7p = -10p - 14 -p + 22 = -10p - 14 9p + 22 = -14 9p-example-1
User Llihttocs
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1 Answer

18 votes
18 votes

9514 1404 393

Answer:

(c) identity property of addition

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)