Section 3-4 Solve Multistep Inequalities

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)SimplifySubtraction Property of Inequality (put constant terms on the other side)Simplify

Division Property of Inequality

Simplify

Real-world and InequalitiesJose 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) ≥ 60015h ≥ 1200

h ≥ 80Jose must work at least 80 hours.

Real-world and InequalitiesTia 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 < 6Tia must buy less than 6 pounds of trail mix.

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Real-world and InequalitiesAn 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

Real-world and InequalitiesMel 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