Question

The Division Property of Equality says that for every real number​ a, b, and​ c, if ab and c​0, then . Why does the property state that c​0? Question content area bottom Part 1 Choose the correct answer below. A. When c​0, both sides of the equation are undefined and undefined expressions do not equal anything. B. When c​0, both sides of the equation are equal to​ 0, so the equation is true even if ab. C. When c​0, both sides of the equation are​ undefined, so the equation is true even if ab. D. When c​0, both sides of the equation are equal to​ 0, so the equation is false even if ab.

Answer 1

B. When c > 0, both sides of the equation are equal to 0, so the equation is true even if ab.

Explanation:

The correct answer is:

B. When c > 0, both sides of the equation are equal to 0, so the equation is true even if ab.

The Division Property of Equality states that if you have an equation of the form a = b, then you can divide both sides of the equation by a non-zero number, c, to get the equivalent equation a/c = b/c. In the context of this question, it means that if ab and c > 0, then a/c = b/c is a true statement.

When c > 0, both sides of the equation a/c = b/c are equal to 0, and dividing by a positive number doesn't change the truth of the equation. This is why the property states that c > 0.