Question

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

13x−4=−9(4+3x)+12

Answer 1

Answer:

1. distributive property
2. properties of numbers (12-36 = -24)
3. addition property of equality

Step-by-step explanation:

1. The first step is elimination of parentheses. That is accomplished by making use of the distributive property—multiplying everything inside parentheses by the multiplier outside.

2. The numbers -36 and +12 are combined in this step to make -24. The ability to do so comes from the properties of real numbers: you can add them.

3. In this step, we added 4 to both sides of the equation. The addition property of equality lets us do that without compromising the truth of the equal sign. (Just as in the previous step where we added 27x to both sides.)