Given, 4x + 7 = 6x + 17, what property of equality would you use to solve this problem? How many times?

Step-by-step 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

So, the addition property of equality may be used once or twice, and the multiplication property of equality is used once.