Day 8 Quiz and Inequalities

Warm – Up 1. Write an equivalent expression for: 4x + 6d – 7x + 8 – d + 12 2. Solve the equations: a) 5x + 12 = 2(x+4) b) 12x + 8 = 15x + 3 + 5 – 3x

HW 1.7 Check

Quiz – You have 25 minutes to complete!

Inequalities Complete the Statement: < means__________________ > means__________________ = means__________________

How many solutions do most inequalities have. Infinite How many solutions do most inequalities have? Infinite! (More than 1 million – cannot count the total number)

Less Than and Is Less Than have DIFFERENT MEANINGS X less than 3 means 3 - x X is less than 3 means X < 3

Evaluating inequalities to identify solutions

Graphing Inequalities: Remember Variable MUST be on the LEFT LEss than is LEft gReateR is Right

Graph -1 on the number line Graph -1 on the number line. How would I show that a number is less than -1?

Graphing solutions to inequalities The solution is not just one number therefore we can graph the solution to represent all solutions

Graphing Create a number line with at least 3 numbers on it. The number given in the inequality and one number less than it and one number greater than it. Graph a circle (open/closed) on the number in the inequality Shade according to the less than or greater than symbol

Reminders: Closed circle if inequality has: Open circle if inequality has:

If the variable is on the LEFT SHADE as if the symbol were an arrow If the Variable is on the Right Rewrite the inequality so that the variable is on the LEFT

Ex. X > -2 2. S < 5 3. 4.

Write an inequality to show that Kyle is older than Jaime

Exs. 2. **Remember** LEss than is LEft gReateR is Right

Canadian Speed Limit Sign limit sign Australian 60kmh speed limit sign US speed limit sign

Solve (solve like you would solve an equation!) 1.

Solve and graph each example 2. 3.

4. Subtracting to solve

When you multiply or divide by a negative number you ALWAYS flip the inequality symbol!!! 5. 6.

Word Problems 1. The maximum safe load of a chairlift is 680 lbs. The weight of the person in the lift is 124 lbs, and the weight of the bicycle is 32 lbs. How much additional weight can the chairlift safely carry?

2. Your baseball team has a goal to collect at least 106 blankets for a shelter. Team members brought 42 blankets on Monday and 65 blankets on Wednesday. How many blankets must the team donate on Friday to make or exceed their goal?

3. In order to receive a B in your literature class, you must earn more than 350 points of reading credits. Last week you earned 120 points. This week you earned 90 points. How many more points must you earn to receive at least a B?

4. The track team at Hale High School plans to sell t-shirts to raise money for new equipment. In order for the track team to make a profit, the income from selling the T- shirts must be greater than the cost of making the T-shirts. At Ted’s Tees, printing costs are $0.80 per shirt and the cost for each T-shirt is $3.75. The shop also charges a $125 fee per order for the silk-screen design. Write an inequality to represent this situation.

5. Mr. Gleason is opening a new restaurant. He has enough booths to seat up to 40 people. He is ordering tables to fill up the rest of the seating space. Each table can seat up to 6 people.  Questions: 1) If t represents the number of tables Mr. Gleason orders, write an expression to show the total number of people that can be seated at booths and tables. Explain you reasoning.   2)Write and inequality that could be used to determine, t, the number of tables Mr. Gleason needs to order so that he has enough seating at booths and tables for at least 125 people. Explain your reasoning. 3) Solve the inequality from the previous question to determine the number of tables Mr. Gleason needs to order. Show or explain how you got your answer.

Complete the 4 word problems

Homework 1.8