Chapter 4

Inequalities

4.1 Inequalities and Their Graphs

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

≤

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 greaterthan or

equal to B.

Ex 1: Determine whether the given number is a solution of the inequality of

x >4a.) 4

4>4

False

b.) 0

0>4

False

c.) -4

-4>4

False

d.) 6

6>4

True

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

Graph the Inequality on the # line

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

2. Put a circle on the number.

Open Circle if < or >.

Solid Circle if “or equal to” ≤or≥.

Ex 2: Graph the solution ofx > -2

-2-6 -4 0 642

Ex 3: 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

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

x>5

Now graph it

Ex 4: This is the graph of:

1) x -2

2) x > -2

3) x -2

4) x < -2

-2-6 -4 0 642

Ex 5: This is the graph of:

1) x 1

2) x > -1

3) x -1

4) x > 1

-2-6 -4 0 642

4.2

The Addition Property of Inequalities

Addition Property of InequalitiesIf a < b, then

a + c < b + c

The same is true for >, , and

Ex 6: Solve for “x”and graph:x - 3 > 4

+3 +3

X > 7

-4 -8 0 84

Ex 7: Solve for “x” and graph:

8z + 6 – 7z 16

Z + 6 16-6

z 10

-4 -8 0 84

-6

Ex 8: Solve: 1 1

3 4x

4 3

12 12x

3 4

12 12x

7

12x

Ex 9: 5(y-2)-4(y-1)<0

Assignment:Page 173 (4-18, 26-30) even

Page 178 (8-36) even