1 Soccer 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? Solving Multi-Step Inequalities 3.6 LESSON

2 To solve a multi-step inequality like 2x + 1 > 5, you should use the properties of inequality to get the variable terms on one side of the inequality and the constant terms on the other side. Solving Multi-Step Inequalities 3.6 LESSON

3 Let g represent the average number of goals scored per game. Write a verbal model. Writing and Solving a Multi-Step Inequality EXAMPLE 1 Find the average number of goals your team needs to score per game to break the school record, as described on the previous slide. SOLUTION Goals scored this season + School record Goals scored per game Number of games left > g > 138 Substitute. Solving Multi-Step Inequalities 3.6 LESSON

g > 138 Writing and Solving a Multi-Step Inequality EXAMPLE 1 Find the average number of goals your team needs to score per game to break the school record, as described on the previous slide. SOLUTION g > 138 Substitute. – 88 – 88 10g > 50 Simplify. Subtract 88 from each side. Divide each side by 10. g > 5 Simplify. ANSWER Your team must score, on average, more than 5 goals per game. Solving Multi-Step Inequalities 3.6 LESSON 10g > 50 > 10

5 Solving a Multi-Step Inequality EXAMPLE 2 Simplify. Add 6 to each side. Multiply each side by –4. Reverse the inequality sign. Simplify. Original inequality. – 6 – 5 x –4 > – 6 – 5 x –4 > x –4 > 1 x > x –4 < – 4 – 4 1 x –4 < Solving Multi-Step Inequalities 3.6 LESSON

6 You have two options: buying skates or renting skates. Let v represent the number of visits to the skating rink. Write a variable expression for the cost of each option. Combining like Terms in a Multi-Step Inequality EXAMPLE 3 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? v 5v + 4v, or 9v Skate rental fee + Number of visits Admission fee Number of visits Option 2 : Renting Skates Cost of skates + Number of visits Admission fee Option 1 : Buying Skates Solving Multi-Step Inequalities 3.6 LESSON SOLUTION

7 To find the values of v for which the cost of option 1 is less than the cost of option 2, write and solve an inequality. Combining like Terms in a Multi-Step Inequality EXAMPLE 3 SOLUTION v 5v + 4v, or 9v Skate rental fee + Number of visits Admission fee Number of visits Option 2 : Renting Skates Cost of skates + Number of visits Admission fee Option 1 : Buying Skates Cost of option 1 (Buying skates) < Cost of option 2 (Renting skates) Simplify v < 9v Solving Multi-Step Inequalities 3.6 LESSON

8 Combining like Terms in a Multi-Step Inequality EXAMPLE 3 Divide each side by 5. Simplify. Subtract 4v from each side. – 4v – 4v45 + 4v < 9v 45 < 5v 55 < 9 < v ANSWER If you buy skates, the cost will be less after more than 9 visits. Simplify v < 9v Cost of option 1 (Buying skates) < Cost of option 2 (Renting skates) Solving Multi-Step Inequalities 3.6 LESSON