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 ( , 3.45978) R: Real (all rational and irrational)

Real Numbers, R IMAGINARY   Irrational Rational Integers Whole Natural

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

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

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

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

Linear Inequalities in One Variable

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.

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.

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.

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.

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

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

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

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

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.

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

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

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

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