Real numbers in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Which properties of the real numbers are being used in the following equalities? (Choose between: commutativity, associativity, distributivity over addition, here (x,y) are real numbers):

1. (3(x+4y)=3x+12y)

2. (4+(x+y)=(4+x)+y)

3. (3+x=x+3)

Exercise 2.

Let (x,yinmathbb R) be such that (x>y). Is it true or not that (xge y)?