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If a < 0 and c > b, circle the expression that is greater:
a(b - c) or a(c - b)
Use the properties of inequalities to explain your choice.

Respuesta :

lyndalau86

Answer:

The expression that is greater is a (b - c)

Step-by-step explanation:

  • a < 0 and c > b, this means (by the addition property) that c - c > b - c⇒0 > b - c

so for the product a(b - c) we would have a multiplication of a negative number a and another negative number (b - c). We know that the result of the multiplication of two negative numbers  is a positive number.

Therefore, a (b - c) > 0

  • a < 0 and c > b, this means by the addition property that c - b > b - b⇒ c - b > 0

so for a(c - b), we have the negative number a multiplied by the positive number (c - b). We know that the result of the multiplication of a negative number by a positive number is negative.

Therefore  a (c - b) < 0

Thus, the expression that is greater is the positive one which is a (b - c)

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