which property of real numbers is illustrated by the following statment?

-6x(17+14)= -6(17)+(-6)(14)

The distributive property.

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Another 2009 question?

The property of real numbers illustrated by the statement -6x(17+14) = -6(17) + (-6)(14) is the distributive property.

The distributive property states that for any real numbers a, b, and c, the product of a and the sum (or difference) of b and c is equal to the sum (or difference) of the products of a and b, and a and c. In other words, a(b + c) = ab + ac.

In the given statement, we have -6x(17+14), which can be simplified using the distributive property. We distribute -6x to both terms inside the parentheses:

-6x(17+14) = -6x(17) + (-6x)(14)

By applying the distributive property, we obtain the equation on the right side: -6(17) + (-6)(14). This shows that the original expression can be simplified to the sum of the products of -6 and 17, and -6 and 14.