Section 3-4 Solve Multistep Inequalities

Section 3-4 Solve Multistep Inequalities

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Section 3-4 Solve Multistep Inequalities

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1. Section 3-4 Solve Multistep Inequalities • Objectives: • Solve multi-step inequalities with variables on one or both sides Solve inequalities as you do equations except: If you multiply or divide by a negative number change the inequality sign

2. Solve Multi-step Inequalities • 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 Solve the inequality Notice the sign did not change Subtract 7 from both sides Simplify Division Property of Inequality Simplify

3. Solve using the Properties of Inequalities Do Now Solve the inequality 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

4. Business 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 – (490 + 45 + 65) ≥ 600 Solve the problem: 15h – (600) ≥ 600 15h ≥ 1200 h ≥ 80 Jose must work at least 80 hours.

5. Budgeting Real-world and Inequalities Tia brings \$26 to the grocery store to buy x pounds of trail mix. Each pound of trail mix costs \$3. If Tia wants to have more than \$8 left over, how much trail mix can she buy? Write and solve an inequality with x. Graph the solution on a number line. Define a variable: x=number of pounds of trail mix Write an inequality to model the problem: 26 – 3x > 8 Solve the problem: 26 – 3x > 8 -3x > -18 x < 6 Tia must buy less than 6 pounds of trail mix. 0 1 2 3 4 5 6

6. You Try Real-world and Inequalities An inchworm is crawling up a tree. It begins 18 inches above the ground and climbs up 3 inches every minute. Let t represent the number of minutes since the worm began climbing. Write and solve an inequality to determine when the inchworm be more than 60 inches above the ground. Inequality: 3t + 18 > 60 Solution: t > 14

7. You Try Real-world and Inequalities Mel works as a waiter. He uses the linear expression 4x + 5 to calculate his hourly earnings, in dollars, based on the number of tables, x, that he serves. Solve the inequality 4x + 5 > 25 to determine how many tables he must serve per hour in order to earn more than \$25 per hour. Solution: x > 5