Chapter 4 Lesson 1

Inequalities and their Graphs

Objectives and Standards

• Objectives1. Identify solutions of inequalities2. Graph and write inequalities

• Standards1. M11.D.1.1.3

Vocabulary

• Inequality – is a range of values identifiable by < (less than), > (greater than), (less than OR ≦equal to), and (greater than OR equal to) ≧instead of an equal sign (which denotes an equation)

• A solution of an inequality is any value or values of a variable in the inequality that makes the inequality true

Identifying Solutions by Evaluating

• Is each number a solution of 3 + 2x < 8?a) -2 b) 3 3 + 2(-2) < 8 Substitute in for x 3 + 2(3) < 8 3 – 4 < 8 Simplify 3 + 6 < 8 -1 < 8 Compare 9 < 8 -2 is a solution 3 is not a solution

Try on your own

• Is each number a solution of 2 – 5x > 13?a) 3 b) -4

Quick Check

1. Is each number a solution of x -4.1?≧a) -5 b) -4.1 c) 8 d) 0

2. Is each number a solution of 6x -3 > 10?a) 1 b) 2 c) 3 d) 4

Graphing Inequalities

• Graphing > OR < - To graph either less than or greater than, you must plot the point as an OPEN circle to show it does not include that point. Then color in the correct direction

• Graphing OR ≦ ≧ - To graph either less than OR equal to or greater than OR equal to, you must plot the point as a CLOSED circle to show that it does include the point. Then color in the correct direction.

Graphing Inequalities

• Graph the Inequalitiesa) d < 3 the solutions of d < 3 are all to the left of 3

b) -3 g The solutions of -3 g are ≧ ≧ -3 and all the points to the left of -3

1 2 3 4 5-1 0

-2 -1 0 1 2-4 -3

Example Try on your own

• Graph each Inequality a) c > 2

b) 4 m ≦

Writing an Inequality from a graph

a) x < 2 Numbers are less than 2 are graphed

b) x ≦ -3 Numbers equal to OR less than -3 are graphed

1 2 3 4 5-1 0

-2 -1 0 1 2-4 -3

Quick Check

2. Graph each inequalitya) a < 1

b) n -3≧

c) 2 > p

Try on your own

3. Write an inequality for each grapha) b)