1 – 6 Solving Linear Inequalities Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.

The following are examples of inequalities in one variable. 5y + 1 < 11 10c + 20  40 12d – 24  60 A solution of an inequality in one variable is a value that makes the inequality true.

To graph an inequality in one variable, use an open dot for < or > and a closed dot for  or . 1. Graph x < 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2. Graph x  -2 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Solving an inequality with a variable on one side and graph Solve: Now, + 9 Then, ÷ by 11 Graph y > 2

Solving an inequality with a variable on both sides and graph. Solve: Now, Graph the solution.

Solving a compound inequality A compound inequality is two simple inequalities joined by “and” or “or”. #1. (and) Graph #2. Graph

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

Solving an “and” compound inequality Solve: Graph:

Solving an “or” compound Inequality Solve Solution of first inequality

Solution of second inequality: Graph:

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

HOMEWORK: P.

Transformations that produce equivalent inequalities 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 that produce equivalent inequalities 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 inequality The percentage of house holds, h, with cable television is modeled by: where y is the number of years since 1998. Describe the years when the percentage is less than 53.2

The percentage is less than 53.2 for the years before 2002.

Using an “and “ compound 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:

Using an “or” compound 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