Inequalities and Their Graphs

Topics for Today:

We moved on to Chapter 3 today.  Our discussion has moved from equations where both sides are equal, to inequalities where one side is larger or smaller than the other.  We also discussed the difference between solutions where the endpoint is included vs excluded and explored the graphs of inequalities.  A solution to an inequality is any value that will make the inequality true.  Inequalities differ from equations because inequalities often have infinite solutions that are bound by a particular value whereas equations typically have a finite solution set.

Graphic Credit: https://www.katesmathlessons.com/graphing-inequalities.html

Vocabulary: inequality, solution to an inequality

Sections Covered in Textbook:

3-1: Inequalities and Their Graphs (pages 134-138)

Resources & Tutorials:

1) What is an Inequality?
2) How Do You Graph Inequalities?
    (This video also includes infinite sets which we did not discuss.)

Exploring Real Numbers

Topics for Today:

We are still working on the language of Algebra and using precise words.  Today we discussed the different classifications for numbers and what sets various types of numbers belong to (Natural, Whole, Integers, Rational, Irrational, and Real).  We also reviewed the meaning of absolute value.

Vocabulary: natural numbers, whole numbers, integers, rational number, irrational number, real numbers, inequality, opposites, absolute value

Sections Covered in Textbook:

1-3: Exploring Real Numbers (Pages 17-23)

Resources & Tutorials:

1) What is a real number?
2) What is a rational number?
3) What are natural and whole numbers?