Determine if each statement is true or false. if the statement is false, explain why, or show work proving that it is false.
a. if a = 5, then ac = 5c.
b. if ac = 5c, then a = 5.

a). true

b). true

Step-by-step explanation:

a).

Given : If a = 5, then ac = 5c

            Let c be any constant.

            a = 5 (given)

            Therefore, ac = 5c

Here a  is given a constant value (5), also let assume c to be a constant. So when we multiply each term we will get a constant value of 5c. The ratio does not change.

Hence proved.

b).

Given : If ac = 5c, then a = 5

            Let c be any constant

            It is given, a = 5

Therefore, ac = 5c

Here the product of two terms is given as 5c, where c is assume to be a constant. Then as a product rule, the value of a will be 5. The ratio will not change.

Hence proved.

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