Skill Check Lesson Presentation Lesson Quiz

Skill Check Solve. 1. x – 5 = –4 1 2. 23 = d + 7 16 3. 4. a > 40

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?

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.

1 + • 88 + 10g > 138 Writing and Solving a Multi-Step Inequality EXAMPLE 1 Writing and Solving a Multi-Step Inequality 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 Let g represent the average number of goals scored per game. Write a verbal model. Goals scored this season + School record • per game Number of games left > 88 + 10g > 138 Substitute.

1 88 + 10g > 138 88 + 10g > 138 – 88 – 88 10g > 50 > EXAMPLE 1 Writing and Solving a Multi-Step Inequality 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 88 + 10g > 138 Substitute. 88 + 10g > 138 – 88 – 88 Subtract 88 from each side. 10g > 50 Simplify. 10g > 50 > 10 Divide each side by 10. g > 5 Simplify. ANSWER Your team must score, on average, more than 5 goals per game.

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

EXAMPLE 3 Combining like Terms in a Multi-Step Inequality 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? SOLUTION 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. Cost of skates + • Number of visits Admission fee Option 1: Buying Skates 45 + 4v Skate rental fee + • Number of visits Admission fee Option 2: Renting Skates 5v + 4v, or 9v

EXAMPLE 3 Combining like Terms in a Multi-Step Inequality SOLUTION 45 + 4v 5v + 4v, or 9v Skate rental fee + • Number of visits Admission fee Option 2: Renting Skates Cost of skates Option 1: Buying Skates 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. Cost of option 1 (Buying skates) < Cost of option 2 (Renting skates) 45 + 4v < 9v Simplify.

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

Solve the inequality. Graph your solution. Lesson Quiz 1. Is –3 a solution of ? yes Solve the inequality. Graph your solution. 2. 2 + 3k > 35 k > 11 8 10 12 14 16 3. m –9 – 14 –12 –10 –8 –6 4. Challenge Find all the values of x that make both of the following inequalities true: 5 < 4x + 13 and 8 + 3x 20. –2 < x 4