Question

What is the reason for each step in the solution of the equation?

−6x = −2 (x + 12)

Drag and drop the reasons into the boxes to correctly complete the table.

−6x = −2 (x + 12) ________________________

−6x = −2x − 24 ________________________

−4x = −24 _________________________________

x = 6 _________________________________

Distributive Property or Division Property of Equality or Associate Property or Given, or Addition Property of Equality

Answer 1

−6x=−2(x+12) is Given

−6x=−2x−24 is Distributive Property

−4x=−24 is Addition Property of Equality

x=6 is Division Property of Equality

Answer 2

Given; Distributive Property; Addition Property of Equality; Division Property of Equality

Explanation:

The first line is the equation we are originally given; this makes the reason for the statement "Given."

To get the statement on the second line, both x and 12 have been multiplied by -2. The property that allows us to do this is the distributive property.

To get the statement on the third line, we must cancel the -2x. We do this by adding; the property that allows us to do this is the addition property of equality.

To get the last statement, we must divide both sides by -4. The property that allows us to do this is the division property of equality.