Answer:
- addition property of equality 2 times (or one)
- multiplication property of equality 1 time
Explanation:
The addition property of equality is used to separate constant and variable terms. It is often used in two steps, one for variable terms and one for constant terms:
4x +7 = 6x +17 . . . . given
7 = 2x +17 . . . . . . . . add -4x to both sides (one use of addition property)
-10 = 2x . . . . . . . . . . add -17 to both sides (another use of addition prop.)
-5 = x . . . . . . . . . . . multiply both sides by 1/2 (multiplication property)
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Alternate Solution
The addition property can be used only once by doing both additions at the same time:
4x +7 -(4x+17) = 6x +17 -(4x +17) . . . . use the addition property once
-10 = 2x . . . . . simplify the above
-5 = x . . . . . . . use the multiplication property of equality once
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So, the addition property of equality may be used once or twice, and the multiplication property of equality is used once.