pg. 409 test prep #50-53 all - rvrhs

Warm-Up

Pg. 409

Test Prep

#50-53 all

Warm-Up

Pg. 409

Test Prep

#50 A

#51 H

#52 D

#53 F

Homework Questions?

Section 7.5 Practice

Section 7.5 Re-Teaching Worksheet

What will you learn?

I’ll be able to explain how to graph linear

inequalities and to use linear inequalities

when modeling real-world situations.

Linear Inequalities

Lesson 7-5 Practice

Please work on #1-3

Linear Inequalities

Lesson 7-5 Practice

Linear Inequalities

Lesson 7-5 Practice

Suppose you can spend up to $10 on bananas and apples. Apples cost $3 per

pound and bananas cost $1 per pound. Write and graph a linear inequality. List

three possible combinations of apples and bananas you can buy.

Linear Inequalities

Lesson 7-5 Practice

Relate: cost of plus cost of is less than total budget apples bananas or equal to

Define: Let a = the number of pounds of apples.

Let b = the number of pounds of bananas.

Write: 3 a + 1 b 10 < –

(continued)

Linear Inequalities

Lesson 7-5 Practice

Graph 3a + 1b 10 by graphing the

intercepts (3.33, 0) and (0, 10). The coordinates of the points on the

boundary line make the inequality true.

So, use a solid line. Graph only in Quadrant I, since you

cannot buy a negative amount of fruit.

< –

Test the point (0, 0).

3a + 1b 10

3(0) + 1(0) 10 Substitute (0, 0) for (a, b).

0 10 Since the inequality is true, (0, 0) is a solution.

< – < – < –

Number of pounds of apples

Nu

mb

er

of p

ou

nd

s o

f b

an

an

as

(continued)

Linear Inequalities

Shade the region containing (0, 0). The graph below shows all the possible

solutions of the problem.

Since the boundary line is included in

the graph, the intercepts are also

solutions to the inequality.

The solution (1, 6) means that if you

buy 1 pound of apples with 6 pounds

of bananas. Two more solutions are

2 pounds of apples with 2 pounds of

bananas and 2 pounds of apples with

4 pounds of bananas.

Lesson 7-5 Practice

Number of pounds of apples

Nu

mb

er

of p

ou

nd

s o

f b

an

an

as

Trent is going to make a rectangular garden in his yard. He wants the perimeter

to be no larger than 40ft. Write and graph a linear inequality. What are three

possible sets of dimensions that the garden can have?

Linear Inequalities

Lesson 7-5 Practice

Relate: twice the plus twice the is less than perimeter length width or equal to

Define: Let l = the length of the rectangular garden.

Let w = the width of the rectangular garden.

Write: 2 l + 2 w 40 < –

(continued)

Linear Inequalities

Lesson 7-5 Practice

Graph 2l + 2w 40 by graphing the

intercepts (20, 0) and (0, 20). The coordinates of the points on the

boundary line make the inequality true.

So, use a solid line. Graph only in Quadrant I, since you

cannot have a negative measurement.

< –

Test the point (0, 0).

2l + 2w 40

2(0) + 2(0) 40 Substitute (0, 0) for (l, w).

0 40 Since the inequality is true, (0, 0) is a solution.

< – < – < –

Length (ft)

Wid

th (

ft)

(continued)

Linear Inequalities

Shade the region containing (0, 0). The graph below shows all the possible

solutions of the problem.

Since the boundary line is included in

the graph, the intercepts are also

solutions to the inequality.

The solution (8, 6) means that you

can have a length of 8ft and width of

6 ft. Two more solutions are 2 ft by

10 ft rectangle and 14 ft by 4 ft

rectangle..

Lesson 7-5 Practice

Length (ft)

Wid

th (

ft)

Section 7.6 Practice Systems of Linear

Inequalities

What will you learn?

I’ll explain how to model real-world

situations using systems of linear

inequalities.

Systems of Linear Inequalities

Example 1 Suppose you buy flour and cornmeal in bulk to

make flour tortillas and corn tortillas. Flour costs $1.50/lb. Cornmeal

costs $2.50/lb. You want to spend less than $9.50 on flour and

cornmeal, and you need at least 4 lb altogether.

Lesson 7-6

Define: Let f = lbs of flour.

Let c = lbs of cornmeal.

Relate: The amount is less 9.50. The total is at 4. spent than lbs least Write:1.5 f +2.50 c 9.50 f + c 4 > – <

Additional Examples


(continued)

Three examples are 5 lbs of cornmeal

and 1 lb of flour, 1 lb of cornmeal and

4 lbs of flour, or 2 lbs of cornmeal and

2 lbs of flour.

Solve by graphing. 1.5f + 2.5c 9.5

f + c 4

Lesson 7-6

> –

<

Additional Examples B

ag

gin

g

Cornmeal (lbs)

Flo

ur

(lb

s)


Example 2 Suppose you have a job in an ice cream shop that

pays $6 per hour. You also have a babysitting job that pays $4 per

hour. You want to earn at least $60 per week but would like to work

no more than 12 hours per week. Write a system of inequalities that

describe this situation. Graph the system to show all possible

solutions. Give three possible solutions.

Lesson 7-6

Define: Let c = hours working at the ice cream shop

Let b = hours working at babysittnig

Relate: The hours is at 12. The total is at 60. worked most amount least earned Write: c + b 12 6 c + 4 b 60 > – <

Additional Examples

–


(continued)

Three examples are working 11 hours

in the ice cream shop and 1 hour

babysitting, 10 hours in the ice cream

shop and 2 hours babysitting, or 8

hours in the ice cream shop and 3

hours babysitting.

Solve by graphing. c + b 12

6c + 4b 60

Lesson 7-6

> –

<

Additional Examples B

ag

gin

g

Ice Cream Shop (hours)

Ba

bysittin

g (

ho

urs

)

–

Warm-Up Quiz You will have 10 minutes to complete the 7.5-7.6 quiz.

Journal Entry

• TOPIC: 7.5-7.6 Practice

• Answer the following question: After today’s

class, explain if you have a better

understanding applications

using systems of equations.

Clear your calculators! Take out your agendas! Copy down DUE DATES! Homework: Section 7.5-7.6 Practice WS

pg. 409 test prep #50-53 all - rvrhs

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