1. Properties of Real Numbers
N: Natural (1,2,3, …)
W: Whole (0,1,2,3,…)
Z: Integers (… -2,-1,0,1,2,…)
Q: Rationals (m/n; m,n integers)
I: Irrational ( , )
R: Real (all rational and irrational)

2. Real Numbers, R
IMAGINARY
Irrational
Rational
Integers
Whole
Natural

3. Comparing 2 Real Numbers
Simplify if Possible
Approximate Irrational Numbers & fractions as a decimal (Remember: a fraction is just division)
Determine the larger of two numbers and place the appropriate inequality between them

4. Comparing 2 Real Numbers
Compare and 3.8 using < or > or

5. Comparing 3 Real Numbers
Simplify if possible
Approximate Irrational Numbers & fractions as a decimal (Remember: a fraction is just division)
Rewrite them left to right in ascending order
Put a less than symbol (<) between them

6. Comparing 3 Real Numbers
Compare , 5, and 4 using < or >

7. Linear Inequalities in One Variable

8. Linear Inequalities in One Variable
Graphing intervals on a number line
Solving inequalities is closely related to solving equations. Inequalities are algebraic expressions related by
We solve an inequality by finding all real numbers solutions for it.

9. Linear Inequalities in One Variable
Graphing Intervals Written In Interval
Notation on Number Lines
EXAMPLE 1
Write the inequality in interval notation and graph it.

10. Linear Inequalities in One Variable
Graphing Intervals Written In Interval
Notation on Number Lines
EXAMPLE 2
Write the inequality in interval notation and graph it.
Copyright © 2010 Pearson Education, Inc. All rights reserved.

11. Linear Inequalities in One Variable
Solving Linear Inequalities Using the Addition Property
Solving an inequality means to find all the numbers that make the inequality true.
Usually an inequality has a infinite number of solutions.
Solutions are found by producing a series of simpler equivalent equations, each having the same solution set.
We use the addition and multiplication properties of inequality to produce equivalent inequalities.
Copyright © 2010 Pearson Education, Inc. All rights reserved.

12. 3.1 Linear Inequalities in One Variable
Using the Addition Property of Inequality
Solve and graph the solution:

13. Linear Inequalities in One Variable
Using the Addition Property of Inequality
Solve and graph the solution:

14. Linear Inequalities in One Variable
Using the Multiplication Property of Inequality
Solve and graph the solution:

15. Linear Inequalities in One Variable
Using the Multiplication Property of Inequality
Solve and graph the solution:

16. Solving a Linear Inequality
Steps used in solving a linear inequality are:
Step 1 Simplify each side separately. Clear parentheses, fractions, and decimals using the distributive property as needed, and combine like terms.
Step 2 Isolate the variable terms on one side. Use the additive property of inequality to get all terms with variables on one side of the inequality and all numbers on the other side.
Step 3 Isolate the variable. Use the multiplication property of inequality to change the inequality to the form x < k or x > k.

17. Linear Inequalities in One Variable
Solving a Linear Inequality
Solve and graph the solution:

18. Linear Inequalities in One Variable
Solving a Linear Inequality with Fractions
Solve and graph the solution:

19. Linear Inequalities in One Variable
Solving a Three-Part Inequality
Solve and graph the solution:

20. Linear Inequalities in One Variable
Solving a Three-Part Inequality
Solve and graph the solution: