Section 3-4 Solve Multistep Inequalities SPI 23A: Solve multi-step inequalities in real-world situation Objectives: Solve multi-step inequalities with variables on one or both sides

Solve the inequality Solve Multi-step Inequalities Subtract 7 from both sides Simplify Undo all addition and subtraction first Then undo all multiplication and division Remember to change the sign if multiplying or dividing by a negative number Division Property of Inequality Simplify

Solve the inequality Solve using the Properties of Inequalities Simplify first using distributive property Subtraction Property of Inequality. (put variables on one side) Simplify Subtraction Property of Inequality (put constant terms on the other side) Simplify Division Property of Inequality Simplify

Real-world and Inequalities Jose is starting a word-processing business out of his home. He plans to charge $15 per hour. He anticipates his month expenses to be $490 for equipment rental, $45 for materials, and $65 for phone usage. Write and solve an inequality to find the number of hours he must work in a month to make a profit of at least $600. Define a variable:h=number of hours worked Write an inequality to model the problem: 15h – ( ) ≥ 600 Solve the problem: 15h – (600) ≥ h ≥ 1200 h ≥ 80 Jose must work at least 80 hours.