Chapter 4

Inequalities

< Less Than

> Greater Than

4.1 Inequalities and Their Graphs4.2 Addition Property of

Inequalities• To determine if a number is a solution of an

inequality

• To graph inequalities on the number line

• To solve an inequality by adding a number to both sides

An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs:

A solution of an inequality is any value that makes the inequality true. The set of all solutions of an inequality is its solution set.

≤A ≤ B

A is less than or

equal to B.

<A < B

A is lessthan B.

>A > B

A is greaterthan B.

≠A ≠ B

A is notequal to B.

≥A ≥ B

A is greaterthan or

equal to B.

Inequalities vs. EquationsSolutions

Inequality Equation

x + 5 9 x + 5 = 9

x = 4x = 4x = 5

x = 6x 4

x < 3

Is 2 a solution?Thumb up if yes

Thumb down if not a solution

x < 3

Is 0 a solution?Thumb up if yes

Thumb down if not a solution

x < 3

Is -5 a solution?

Thumb up if yes

Thumb down if not a solution

x < 3

Is 3 a solution?Thumb up if yes

Thumb down if not a solution

Graph the solution ofx + 3 = 7

-2-6 -4 0 642

Graph the solution ofx < 3

-2-6 -4 0 642

2.999

-2-6 -4 0 642

3. Draw your solution graph line in the same direction as the inequality IF the “x” is on left.

Graph the solution ofx < -1

1. Draw number line. Label zero and the number where your arrow starts

0-12. Put a circle on the number. Open if < or >. Solid if “or equal to” ≤or≥.

Graph the solution ofx > -2

-2-6 -4 0 642

Graph the solution of

x -2If you have ≤ or ≥ you draw a closed circle

-2-6 -4 0 642

Hint: When graphing make sure your variable is on the left side

5 < x

We would read this as 5 is less than x

How would we graph it?

To make sure the graph is correct switc the variable and number and flip the inequality.

x>5

x is greater than 5

Now graph it

This is the graph of:

1) x -2

2) x > -2

3) x -2

4) x < -2

-2-6 -4 0 642

This is the graph of:

1) x 1

2) x > -1

3) x -1

4) x > 1

-2-6 -4 0 642

Write the inequality shown in this graph

-2-6 -4 0 642

4x

Write the inequality shown in this graph

-2-6 -4 0 642

0x

Addition Property of InequalitiesIf a < b, then

a + c < b + c

“If I add the same number to both sides of an inequality, I get another TRUE inequality in the same direction.”

The same is true for >, , and

Solve for “x”and graph:x - 3 > 4

+3 +3

X > 7

-4 -8 0 84

Solve for “x” and graph:

8z + 6 – 7z 16

Z + 6 16-6

z 10

-4 -8 0 84

-6

Checking: Since there can be an infinite number of solutions to an inequality, it is not possible to check all the solutions. You can check the endpoint and the direction of the inequality symbol.

The solutions of x + 9 < 15 are given by x < 6.

Assignment:-Workbook Page 18 (1-20) all

-Test Sheets Signed-Test Corrections