Part I: Modeling Inequalities

Part I: Modeling Inequalities Let’s model some inequalities. Remember what we’re solving for! 2X + 3 > 5 2x < 12 3X - 7 > 5

Part II: Solving Inequalities

Solving an inequality is very similar to solving an equation. The main difference is that we have an inequality symbol instead of an ____.

Examples 1, 2, & 3: Solve the following inequalities. Graph each solution.

1) p + 6 < 11 2.) - 11 ≥ -4 3) 4y – 12 < 20

4.) If the maximum occupancy of this classroom is 25, how could we show that using an inequality?

5.) Jackson has six $20.00 bills. He is going to buy a pair of Nike Free Run shoes that cost $70.00 and two shirts. Write an inequality for this problem. If Jackson spent all of his money on the shoes and two shirts, how much did he spend on his two shirts?

6.) A theme park has a log ride that can hold 12 people. They also have a weight limit of 1500 lbs per log (which includes the weight of the log) for safety reason. If the average adult weighs 150 lbs, the average child weighs 100 lbs and the log itself weighs 200 lbs. Which inequality below could be used to determine who could ride on the ride? (A = # of adults C = # of children)

a.) 150 + 100 + 200 > 1500 b.) 150A + 100C + 200 < 1500 c.) 150A+100C+200≤1500 d.) 150C + 100A – 200 < 1500 7.) If there are 4 adults already in the log, how many children could ride with them?

8.) Sarah is making a CD for the dance this Friday. The CD will only hold 80 minutes of music. She already has 54 minutes of songs on her CD and would like to put as many songs on it as possible. Considering the average song is four minutes long, how many more songs can she add to her CD before she runs out of space?

9.) What inequality did you use for problem number eight? Could she add 5 songs and not go over the allowed minutes? Could she add 9 songs and not go over the allowed minutes? Explain.

9.) Kristy works as a salesperson at a department store. She is paid $50 per week plus $3 per sale she makes while on the floor. This week, she wants her pay to be at least $100 so she can go to the fair and have money left to buy a new purse. Write an inequality for the number of sales Kristy needs to make, and describe the solutions.

10.) How many sales does Kristy need to top her $100.00 goal?

Algebra Tiles

Model the following equations and inequalities:

1. 3 x + 2 = 8 2. x – 3 = 4

3. 2x – 4 > 8 4. 4x + 3 < 11

5. Jeff makes $4.00 per day babysitting plus $2.00 per lesson that he teaches the students during the day. He wants to make $12 by the end of the day. Write the equality for this problem and show how you would represent that with Algebra- tiles.

Represent your solutions for #3 and #4 on the following number line diagrams:

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7.) Answer Keys

Part I: Modeling Inequalities Let’s model some inequalities. Remember what we’re solving for! 2X + 3 > 5 2x < 12 3X - 7 > 5

2x + 3 – 3 > 5 – 3 2x/2 < 12/2 3X – 7 + 7 > 5 + 7 2x/2 > 2/2 X < 6 3X / 3 > 12 / 3 X > 1 X > 4

x>1 X< 6 X > 4

open

Part II: Solving Inequalities

Solving an inequality is very similar to solving an equation. The main difference is that we have an inequality symbol instead of an equal sign.

Examples 1, 2, & 3: Solve the following inequalities. Graph each solution.

1) p + 6 < 11 2) - - 11 ≥ -4 3) 4y – 12 < 20

P < 5 t > 16 y < 8

4.) If the maximum occupancy of this classroom is 25, how could we show that using an inequality? X < 25

5.) Jackson has six $20.00 bills. He is going to buy a pair of Nike Free Run shoes that cost $70.00 and two shirts. Write an inequality for this problem. If Jackson spent all of his money on the pair of shoes and two shirts, how much did he spend on his two shirts? $70 + 2s < $120 s = $25 per shirt or $50 for both

6.) A theme park has a log ride that can hold 12 people. They also have a weight limit of 1500 lbs ( per log for safety reason. If the average adult weighs 150 lbs, the average child weighs 100 lbs and the log itself weighs 200 lbs. Which inequality below would be used to determine who could ride on the ride? A = # of adults C = # of children

e.) 150 + 100 + 200 > 1500 f.) 150A + 100C + 200 < 1500 g.) 150A+100C+200≤1500 h.) 150C + 100A – 200 < 1500 7.) If there are 4 adults already in the log, how many children could ride with them? C = 7 children

8.) Sarah is making a CD for the dance this Friday. The CD will only hold 80 minutes of music. She already has 54 minutes of songs on her CD and would like to put as many songs on it as possible. Considering the average song is four minutes long how many more songs can she add to her CD before she runs out of space? 54 + 4s < 80 (subtract 54 from both sides) 4s < 26 (divide both sides by 4) S < 8.5 songs 8 more songs

9.) What inequality did you use for problem number six? Could she add 5 songs and not go over the allowed minutes? Could she add 9 songs and not go over the allowed minutes? Explain.

54 + 4s < 80 5 songs = Yes, she would be under the 80 minutes 9 songs = No, He would go over the 80 minutes

10.) Kristy works as a salesperson at a department store. She is paid $50 per week plus $3 per sale she makes while on the floor. This week she wants her pay to be at least $100 so she can go to the fair and have money left to buy a new purse. Write an inequality for the number of sales Kristy needs to make.

50 + 3s > 100

11.) How many sales does Kristy need to top her $100.00 goal?

S > 16.6, so…she would have to make 17 sales to reach her goal

Algebra Tiles

Model the following equations and inequalities: 1. ) 3 x + 2 = 8 2. ) X – 3 = 4

x=2 x=7

3.) 2x – 4 > 8 4.) 4x + 3 < 11

x>6 x>3

2l + 4 = 12 l =4 lessons

Show students how to graph #2 and #3 using the number line and discuss shaded circles and open circles with them (greater than, greater than or equal to, less than, less than or equal to)

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