1. Lesson 3.6 Solving Multi-Step Inequalities
Essential Question: How do you solve multi-step inequalities?

2. Before we start…
Your school’s soccer team is trying to break the school record for goals scored in one season. Your team has already scored 88 goals this season. The record is 138 goals. With 10 games remaining on the schedule, how many goals, on average, does your team need to score per game to break the record?

3. What is an inequality? 𝑥≤6
A statement formed by placing an inequality symbol between two expressions
𝑥≤6

4. Symbol
Meaning
<
Is less than ≤
Is less than or equal to
>
Is greater than ≥
Is greater than or equal to

5. What is a solution of an inequality?
The set of numbers that you can substitute for the variable to make the inequality true

6. What is the graph of an inequality?
Consists of all points on a number line that represent solutions.

7. How do you solve multi-step inequalities?
Use distributive property and/or combine like terms.
Isolate the variable using inverse operations.
Just remember to reverse the inequality symbol when multiplying or dividing by a negative number.

9. Solve and graph 6+ 𝑦 5 <10

12. Solve and graph 6 5−2𝑥 <5𝑥+13

17. Solve and graph 5𝑦+2≤𝑦+34

18. Solve and graph 6+𝑦≥2𝑦−3

19. Ice Skating You plan to go ice skating often this winter
Ice Skating You plan to go ice skating often this winter. The skating rink charges $4 for admission. You can either rent ice skates at the skating rink for $5 per day or buy your own pair for $45. How many times do you have to use the ice skates in order for the cost of buying them to be less than the total cost of renting them?

20. Trip You are organizing a trip to a baseball game
Trip You are organizing a trip to a baseball game. Tickets are $12 per person, and the cost to rent the bus will be divided evenly. Find the possible costs of the bus rental to keep the cost per person under $20 if 30 people sign up to go on the trip.

21. Walk a thon You are collecting sponsors for a 10 mile walk-a-thon
Walk a thon You are collecting sponsors for a 10 mile walk-a-thon. So far, you have collected $230 in donations. How much must the last sponsor pledge per mile to reach or exceed your goal of $300?

22. Dinner and Movie You are going to a dinner and a movie with a group of people. Individual dinners are $7 per person, or the group can pay a lump sum of $105 for a buffet. Tickets to the movie are $5 each. How many people have to attend for the group cost of the buffet dinner and movie to be less than the group cost for individual dinners and a movie?

23. How do you solve multi-step inequalities?

24. Ticket Out the Door
Solve and graph
4𝑥+1>9