1 – 61 – 6Solving Linear InequalitiesSolving Linear Inequalities

Objective:

CA Standard 1: Students solve equations and inequalities involving

absolute value.

The following are examples of inequalities in one variable.

A solution of an inequality in one variable is a value that makes the

inequality true.

1.3x – 2 > 72.5y + 1 < 113.10c + 20 404.12d – 24 60

To graph an inequality in one variable, use an open dot for < or >

and a closed dot for or .

1. Graph x < 3

2. Graph x -2

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

SolvingSolving an inequality with an inequality with a variable on one side a variable on one side

and and graphgraph

Solve: 11 9 13y

11 22y 22

11y 2y

Graph y > 2

Now, + 9

Then, ÷ by 11

Solving an inequality with a Solving an inequality with a variable on both sides and variable on both sides and

graph.graph. Solve: 7 9 10 12x x

9 3 12x 21 3x

Now, Graph the solution.

7 x

Solving a compound Solving a compound inequalityinequality

A compound inequality is two simple inequalities joined by “and” or “or”.

Graph 2 1x

Graph 1 or 2x x

(and)#1.

#2.

-4 -3 -2 -1 0 1 2 3#1.

#2. -4 -3 -2 -1 0 1 2 3

Solving an “and” Solving an “and” compound inequalitycompound inequality

Solve: 2 3 8 10t

6 3 18t 2 6t

Graph: 2 6t

Solving an “or” Solving an “or” compound Inequalitycompound Inequality

Solve 2 3 5 or 4 7 9x x

Solution of first inequality

2 3 5x 2 2x

1x

Solution of second inequality: 4 7 9x

4 16x 4x

Graph:

1 or 4x x

NOTE:NOTE:

Multiplying or Dividing by a negative ALWAYS switches the inequality symbol.

HOMEWORK:HOMEWORK:P.

Transformations that Transformations that produce equivalent produce equivalent

inequalitiesinequalities

1. Add the same number to both sides.

2. Subtract the same number from both sides.

3. Multiply both sides by the same positive number.

4. Divide both sides by the same positive number.

Transformations Transformations that produce that produce equivalent equivalent

inequalitiesinequalities 1. Multiply both sides by the same negative number and reverse the

inequality.

2. Divide both sides by the same negative number and reverse the inequality.

NOTE: Multiplying or Dividing by a negative ALWAYS switches the inequality symbol.

Using a simple Using a simple inequalityinequality

The percentage of house holds, h, with cable television is modeled by: 2.3 44h y where y is the number of years since 1998. Describe the years when the percentage is less than 53.2

53.2 2.3 44y

9.2 2.3y

9.2

2.3y

4 yThe percentage is less than 53.2 for the years

before 2002.

Using an “and “ Using an “and “ compound inequalitycompound inequality

Milk will keep until its expiration date and will not freeze when stored at a minimum temperature of –1 C and a maximum of 5 C. The temperature C that satisfies the inequality – 1 < C < 5. Write the inequality in degrees Fahrenheit Let F represent the temperature in degrees Fahrenheit, and use the formula:

532

9C F

1 5C

51 32 5

9F

932 9

5F

932 41

5F

30.2 41F

Using an “or” Using an “or” compound inequalitycompound inequality

The feeding instructions for your dog’s food recommend 2 ½ to 3 ¼ lb of food weekly.

Write the conditions that represent underfeeding and over feeding your dog as a

compound inequality.

w < 2 ½ or w > 3 ¼

Rewrite the conditions in ounces of dog food.

( 1 lb = 16 oz.)

a < 40 or a > 52