- Slides: 26
Today’s Objective IWBAT solve algebraic inequalities.
What is an inequality? An inequality is an expression that compares two quantities that are not equal using these symbols:
Remember … > The alligator wants to eat the BIGGER AND BETTER TEAM!
Problem 3. 1 Inequalities Caitlyn is shopping online to find a new television for the center. Caitlyn wants a television with at least a 26 -in. screen. Screen Size Price 22 inches $300 26 inches $330 32 inches $370 40 inches $420 Assessment prompt: Take a moment with the partner next to you, write an inequality to show much money, m, the center will need to spend to get at least A 26 -in. screen TV. You have two minutes.
So, your inequality should look like m ≥ $330 Caitlyn drew the graph below to represent the solution to her inequality: 280 300 320 340 360 380 400 420 Why do you think she drew a solid circle at 330?
Inequality Graphs If it’s greater than, the arrow will point to the right If it’s less than, the arrow will point to the left If it’s greater than or equal to OR less than or equal to, the circle must be FILLED IN If it’s just greater than OR less than, the circle will NOT be filled in An inequality graph shows ALL of the solutions possible for the inequality.
Independent Work Raise your hand if you have a question 1. Caitlyn wants to have money left over for accessories. How can Caitlyn change her graph to show that they need to have more than $330? Draw a graph to show much they need to have. 2. The center has a stand for the television that will support up to 30 lb of weight. Draw a graph to show much the TV she buys can weigh.
Now, for the most part … Inequalities can be solved in the same way as equations: 1. ) Add or subtract to get rid of the constant. 2. ) Multiply or divide to get rid of the coefficient. 3. ) Then we have our answer
That sounds EASY PEESY LEMON SQUEEZY!!! Fo reals Ms. Siems? !
So let’s look!
So let’s look … some more!
So let’s look … yet again!
Problem 3. 2 - Part A: Work with your groups and use your roles Caitlyn plans to use money from the community center’s savings account to buy a video game system. She also needs to leave at least $129 in the savings account to buy some softball equipment. Video Game System Sale This Month Only: $250. 00 Selected Extra Games on sale: $35. 00 each
The inequality a – 129 ≥ 250 represents this situation, where a represents the amount of money the center has in its savings account. What does the algebraic expression a – 129 represent? The amount of money that the center already has minus the amount for softball equipment 1. Solve the inequality. What does the solution mean? A ≥ 379, She would need $379 or more to pay for everything 1. Use a number line to show all possible values for a. 1.
A group has $140 to spend. The inequality 15 h + 40 ≤ 140 represents the cost to rent the main hall, where h represents the number of hours the group can rent the room. Solve the inequality. The same group also is considering renting the dining room. Write and solve an inequality to represent this situation. Which room should the group rent? Explain.
Now that you have the hang of it … LET’S KICK IT UP!!!!
Today’s Keypoint If the coefficient is negative, you must:
Let’s Take a Closer Look!!!
Let’s look at one!
Now this one!!!
Problem 3. 3 Part A: With your assigned groups and roles, complete the following questions. There should be ONE master sheet of answers, and each group member should record their answers. The community center has $175 to spend on video games for its new game system. Games are on sale for $35 each. 1. The inequality 174 – 35 g ≥ 0 represents the number of games the center could buy. Solve the inequality and explain the solution. 1. Graph the solution on a number line. 2. Explain why a value of g that is less than zero does not make sense for this situation.
Part B The inequality 175 -8 m ≥ 99 represents the number of months the center could rent games from Net. Games with its $175. Solve the inequality and explain the solution. Graph the solution on a number line. Write and solve an inequality to represent the number of months the center could rent games from Anytime Games. Which service should the community center use? Explain your choice.