2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

Aim 27.3: How do we solve system of inequality word problems by graphing?

Do Now: Shade the following inequality

Take out last night's homeworkHW 27.2

Copy down tonight's homeworkHW - Aim 27.3

y > 2x + 3

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

Directions: Shade the following inequality

3y < ­2x ­ 6

3(    ) < ­2(    ) ­ 6

Mini Lesson

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

3

February 14, 2018

Directions: Shade the following inequality

12x + 10y  > 120  

12(    ) + 10(    ) > 120

Mini Lesson

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

4

February 14, 2018

Directions: Shade the following system of inequalities

9x + 30y  > 180  

x + y < 10

9(    ) + 30(    ) > 180

(    ) + (    )  < 10

Mini Lesson

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

5

February 14, 2018

Directions: Shade the following system of inequalities

20x + 10y  > 200  

x + y < 13

Check for Understanding

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

Steps to translate and graph a systems of inequalities

Step 1:  define your x and y intercepts as specific as possible.

Step 2:  translate the inequalities word for word

Step 3:  solve for the x and the y intercept of each inequality by plugging in "opposite zeros"

Step 4: graph your lines using the intercepts from step 3

Step 5: shade each inequality by testing the point (0, 0) 

true = shade toward  false = shade away

Step 6: locate the solution set (S) by identifying the overlap of the shading and pick a point within that shaded area

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

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Step 1 & 2

1) Alex is buying tree and shrubs for his backyard. The trees costs $40 per tree and the shrubs cost $20 each. He wants to buy at least 12 plants and can spend no more than $400. Write and solve a system of inequalities that describes the situation.

a. What are the variables? b. Write a system of inequalities to represent the situation.

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

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Step 3

1) Alex is buying tree and shrubs for his backyard. The trees costs $40 per tree and the shrubs cost $20 each. He wants to buy at least 12 plants and can spend no more than $400. Write and solve a system of inequalities that describes the situation.

c. Find the x and y intercepts of each inequality.

x intercept x intercept

y intercept y intercept

40x + 20y < 400 x + y > 12

40x + 20( ) > 400 x + ( ) > 12

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

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Step 4, 5 & 6

1) Alex is buying tree and shrubs for his backyard. The trees costs $40 per tree and the shrubs cost $20 each. He wants to buy at least 12 plants and can spend no more than $400. Write and solve a system of inequalities that describes the situation.

d. Graph the inequalities using the x and y intercepts.

0              5         10              15          20

20

15

10

  5

  0

e. Shade each inequality by using the test point (0, 0)

f. Determine a solution. Explain in terms of the situation.

40x + 20y < 400

x < 10y < 20

x + y > 12

x > 12y > 12

40( ) + 20( ) < 400 ( ) + ( ) > 12

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

10

February 14, 2018

Directions: Shade the following system of inequalities

10x + 18y  > 180  

x + y < 12

Exit Slip

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

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February 14, 2018

1) There are tennis ball and baseball on sale at a store. You have at least $200 to spend but need to buy at most 13 boxes. Each tennis ball box cost $20 and each baseball box cost $10. Write and solve a system of inequalities to find how many boxes you can buy.

a. What are the variables?

b. Write inequalities for the given situation

c. Graph the inequalities and shade the solution set.

.

Hw 27.3

2.14.18 ­ Aim 27.3 ­ Solving Inequality Word Problems on a Graph part 2.notebook

12

February 14, 2018

1) There are tennis ball and baseball on sale at a store. You have at least $200 to spend but need to buy at most 13 boxes. Each tennis ball box cost $20 and each baseball box cost $10. Write and solve a system of inequalities to find how many boxes you can buy.

a. What are the variables?

b. Write inequalities for the given situation

c. Graph the inequalities and shade the solution set.

.

Hw 27.3