Solving and Graphing Linear Inequalities Solving One-Step Linear Inequalities

Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO

Did you notice, Some of the dots were solid and some were open? -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Why do you think that is? If the symbol is > or < then dot is open because it can not be equal. If the symbol is  or  then the dot is solid, because it can be that point too.

THE TRAP….. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement.

Solving Using Division Divide each side by the same positive number. 3

Solving by multiplication of a negative # Multiply each side by the same negative number and REVERSE the inequality symbol. Multiply by (-1). (-1) See the switch

Solving by dividing by a negative # Divide each side by the same negative number and reverse the inequality symbol. -2

Let x = the number of minutes used. Example: A cell phone company offers its customers a rate of $89 per month for 350 minutes, or a rate of $40 per month plus $0.50 for each minute used. How many minutes per month can a customer who chooses the second plan use before the charges exceed those of the first plan? Let x = the number of minutes used. Solve the inequality 0.50x + 40  89 . 0.50x  49 Subtract 40. x  24.5 Divide by 0.5. The customer can use up to 24.5 minutes per month before the cost of the second plan exceeds the cost of the first plan. Example: Application