lesson 5 homework practice inequalities answer key

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Explanation:

g - 3 > 4;    6, 7, 8

Is the given value a solution of the inequality?

q — 2 > 16,    q = 20

t - 7 < 10,    t = 28

The table shows the number of different types of roller coasters in the United States. An amusement park wants to build a new roller coaster. They will only build a roller coaster if there are less than 10 of that type in the United States. Use the inequality r < 10, where r is the number of a certain type of roller coaster, to  determine which type(s) can be built.

The table shows the number of different types of movies in Laves collection. He wants to buy a new movie to add to his collection. He only wants to buy a movie  if he already has more than 15 movies of that type. Use the inequality m > 15, where m is the number of the type of movie, to determine which type(s) he can buy.

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The number of text messages Lelah sent each month is shown in the table. She can send no more than 55 messages each month without being charged. Use the  inequality t ≤ 55, where t is the number of text messages in a month, to determine in which months she exceeded her limit. If each additional text costs $0.25, how much was Lelah charged from January to April?

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• Chapter 1 Represent, Count, and Write Numbers 0 to 5
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• Chapter 1 Place Value, Addition, and Subtraction to One Million  (Pages 1- 20)
• Chapter 2 Multiply by 1-Digit Numbers  (Pages 21 – 47)
• Chapter 3 Multiply 2-Digit Numbers  (Pages 49- 65)
• Chapter 4 Divide by 1-Digit Numbers  (Pages 67 – 93)
• Chapter 5 Factors, Multiples, and Patterns  (Pages 95 – 109)
• Chapter 6 Fraction Equivalence and Comparison  (Pages 111 – 129)
• Chapter 7 Add and Subtract Fractions  (Pages 131 – 153)
• Chapter 8 Multiply Fractions by Whole Numbers  (Pages 155- 167)
• Chapter 9 Relate Fractions and Decimals  (Pages 169- 185)
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Grade 4 Homework FL. – Answer Keys

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• Chapter 1: Place Value, Multiplication, and Expressions
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( 3 , 2 ) ( 3 , 2 )

( 2 , 3 ) ( 2 , 3 )

( 3 , 4 ) ( 3 , 4 )

( 5 , −4 ) ( 5 , −4 )

no solution

infinitely many solutions

ⓐ no solution, inconsistent, independent ⓑ one solution, consistent, independent

( 6 , 1 ) ( 6 , 1 )

( −3 , 5 ) ( −3 , 5 )

( 2 , 3 2 ) ( 2 , 3 2 )

( − 1 2 , −2 ) ( − 1 2 , −2 )

( 2 , −1 ) ( 2 , −1 )

( −2 , 3 ) ( −2 , 3 )

( 1 , 3 ) ( 1 , 3 )

( 4 , −3 ) ( 4 , −3 )

( 6 , 2 ) ( 6 , 2 )

( 1 , −2 ) ( 1 , −2 )

ⓐ Since both equations are in standard form, using elimination will be most convenient. ⓑ Since one equation is already solved for x , using substitution will be most convenient.

ⓐ Since one equation is already solved for y , using substitution will be most convenient. ⓑ Since both equations are in standard form, using elimination will be most convenient.

160 policies

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

The angle measures are 55 and 35.

The angle measures are 5 and 85.

The angle measures are 42 and 138.

The angle measures are 66 and 114.

The length is 60 feet and the width is 35 feet.

The length is 60 feet and the width is 38 feet.

It will take Clark 4 hours to catch Mitchell.

It will take Sally 1 1 2 1 1 2 hours to catch up to Charlie.

The rate of the boat is 11 mph and the rate of the current is 1 mph.

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

The speed of the jet is 235 mph and the speed of the wind is 30 mph.

The speed of the jet is 408 mph and the speed of the wind is 24 mph.

206 adults, 347 children

42 adults, 105 children

13 dimes and 29 quarters

19 quarters and 51 nickels

3 pounds peanuts and 2 pounds cashews

10 pounds of beans, 10 pounds of ground beef

120 ml of 25% solution and 30 ml of 50% solution

125 ml of 10% solution and 125 ml of 40% solution

$42,000 in the stock fund and $8000 in the savings account

$1750 at 11% and $5250 at 13%

Bank $4,000; Federal $14,000

$41,200 at 4.5%, $24,000 at 7.2%

ⓐ C ( x ) = 15 x + 25 , 500 C ( x ) = 15 x + 25 , 500

ⓑ R ( x ) = 32 x R ( x ) = 32 x

ⓓ 1,500 1,500 ; when 1,500 benches are sold, the cost and revenue will be both 48,000

ⓐ C ( x ) = 120 x + 150,000 C ( x ) = 120 x + 150,000

ⓑ R ( x ) = 170 x R ( x ) = 170 x

ⓓ 3,000 3,000 ; when 3,000 benches are sold, the revenue and costs are both $510,000

( 2 , −1 , 3 ) ( 2 , −1 , 3 )

( −2 , 3 , 4 ) ( −2 , 3 , 4 )

( −3 , 4 , −2 ) ( −3 , 4 , −2 )

( −2 , 3 , −1 ) ( −2 , 3 , −1 )

infinitely many solutions ( x , 3 , z ) ( x , 3 , z ) where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

The fine arts department sold 75 adult tickets, 200 student tickets, and 75 child tickets.

The soccer team sold 200 adult tickets, 300 student tickets, and 100 child tickets.

ⓐ [ 3 8 −3 2 5 −3 ] [ 3 8 −3 2 5 −3 ] ⓑ [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ] [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ]

ⓐ [ 11 9 −5 7 5 −1 ] [ 11 9 −5 7 5 −1 ] ⓑ [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ] [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ]

{ x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0 { x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0

{ x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3 { x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3

ⓐ [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] ⓑ [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] ⓒ [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ] [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ]

ⓐ [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] ⓑ [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] ⓒ [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ] [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ]

[ 1 −1 2 0 −3 −4 ] [ 1 −1 2 0 −3 −4 ]

[ 1 −1 3 0 −5 8 ] [ 1 −1 3 0 −5 8 ]

The solution is ( 4 , −1 ) . ( 4 , −1 ) .

The solution is ( −2 , 0 ) . ( −2 , 0 ) .

( 6 , −1 , −3 ) ( 6 , −1 , −3 )

( 5 , 7 , 4 ) ( 5 , 7 , 4 )

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number.

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number.

ⓐ −14 ; −14 ; ⓑ −28 −28

ⓐ 2 ⓑ −15 −15

ⓐ 3 ⓑ 11 ⓒ 2

ⓐ −3 −3 ⓑ 2 ⓒ 3

( − 15 7 , 24 7 ) ( − 15 7 , 24 7 )

( −2 , 0 ) ( −2 , 0 )

( −9 , 3 , −1 ) ( −9 , 3 , −1 )

( −6 , 3 , −2 ) ( −6 , 3 , −2 )

infinite solutions

The solution is the grey region.

No solution.

ⓐ { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 ⓑ

ⓐ { a ≥ p + 5 a + 2 p ≤ 400 { a ≥ p + 5 a + 2 p ≤ 400 ⓑ

ⓐ { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 ⓑ

ⓐ { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 ⓑ

Section 4.1 Exercises

( 0 , 2 ) ( 0 , 2 )

( 2 , 4 ) ( 2 , 4 )

( −2 , 2 ) ( −2 , 2 )

( 3 , 3 ) ( 3 , 3 )

( 6 , −4 ) ( 6 , −4 )

No solutions, inconsistent, independent

1 point, consistent and independent

infinite solutions, consistent, dependent

( 1 , −4 ) ( 1 , −4 )

( −3 , 2 ) ( −3 , 2 )

( −1 / 2 , 5 / 2 ) ( −1 / 2 , 5 / 2 )

( −5 , 4 ) ( −5 , 4 )

( 0 , 10 ) ( 0 , 10 )

( 4 , −2 ) ( 4 , −2 )

( 4 , 0 ) ( 4 , 0 )

( 4 , 5 ) ( 4 , 5 )

( 7 , 12 ) ( 7 , 12 )

( −3 , −5 ) ( −3 , −5 )

( 2 , −3 ) ( 2 , −3 )

( −11 , 2 ) ( −11 , 2 )

( 6 / −9 , 24 / 7 ) ( 6 / −9 , 24 / 7 )

infinitely many

ⓐ substitution ⓑ elimination

ⓐ elimination ⓑ substituion

Answers will vary.

Section 4.2 Exercises

−7 −7 and −19 −19

22 and −67 −67

Eighty cable packages would need to be sold to make the total pay the same.

Mitchell would need to sell 120 stoves for the companies to be equal.

8 and 40 gallons

1000 calories playing basketball and 400 calories canoeing

Oranges cost $2 per pound and bananas cost $1 per pound

Package of paper $4, stapler $7

Hot dog 150 calories, cup of cottage cheese 220 calories

Owen will need 80 quarts of water and 20 quarts of concentrate to make 100 quarts of lemonade.

53.5 53.5 degrees and 36.5 36.5 degrees

16 degrees and 74 degrees

134 degrees and 46 degrees

37 degrees and 143 degrees

16 ° 16 ° and 74 ° 74 °

45 ° 45 ° and 45 ° 45 °

Width is 41 feet and length is 118 feet.

Width is 10 feet and length is 40 feet.

1.5 1.5 hour

Boat rate is 16 mph and current rate is 4 mph.

Boat rate is 18 mph and current rate is 2 mph.

Jet rate is 265 mph and wind speed is 22 mph.

Jet rate is 415 mph and wind speed is 25 mph.

Section 4.3 Exercises

110 adult tickets, 190 child tickets

6 good seats, 10 cheap seats

92 adult tickets, 220 children tickets

13 nickels, 3 dimes

42 dimes, 8 quarters

17 $10 bills, 37 $20 bills

80 pounds nuts and 40 pounds raisins

9 pounds of Chicory coffee, 3 pounds of Jamaican Blue Mountain coffee

10 bags of M&M’s, 15 bags of Reese’s Pieces

7.5 7.5 liters of each solution

80 liters of the 25% solution and 40 liters of the 10% solution

240 liters of the 90% solution and 120 liters of the 75% solution

$1600 at 8%, 960 at 6%

$28,000 at 9%, $36,000 at 5.5 % 5.5 %

$8500 CD, $1500 savings account

$55,000 on loan at 6% and $30,000 on loan at 4.5 % 4.5 %

ⓐ C ( x ) = 5 x + 6500 C ( x ) = 5 x + 6500

ⓑ R ( x ) = 10 x R ( x ) = 10 x

ⓓ 1,500; when 1,500 water bottles are sold, the cost and the revenue equal $15,000

Section 4.4 Exercises

( 4 , 5 , 2 ) ( 4 , 5 , 2 )

( 7 , 12 , −2 ) ( 7 , 12 , −2 )

( −3 , −5 , 4 ) ( −3 , −5 , 4 )

( 2 , −3 , −2 ) ( 2 , −3 , −2 )

( 6 , −9 , −3 ) ( 6 , −9 , −3 )

( 3 , −4 , −2 ) ( 3 , −4 , −2 )

( −3 , 2 , 3 ) ( −3 , 2 , 3 )

( −2 , 0 , −3 ) ( −2 , 0 , −3 )

x = 203 16 ; y = –25 16 ; z = –231 16 ; x = 203 16 ; y = –25 16 ; z = –231 16 ;

( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

$20, $5, $10

Section 4.5 Exercises

ⓐ [ 2 4 −5 3 −2 2 ] [ 2 4 −5 3 −2 2 ] ⓑ [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ] [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ]

ⓐ [ 2 −5 −3 4 −3 −1 ] [ 2 −5 −3 4 −3 −1 ] ⓑ [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ] [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ]

{ 2 x − 4 y = −2 3 x − 3 y = −1 { 2 x − 4 y = −2 3 x − 3 y = −1

{ 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2 { 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2

ⓐ [ 3 2 1 4 −6 −3 ] [ 3 2 1 4 −6 −3 ] ⓑ [ 12 8 4 4 −6 −3 ] [ 12 8 4 4 −6 −3 ] ⓒ [ 12 8 4 24 −10 −5 ] [ 12 8 4 24 −10 −5 ]

ⓐ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓑ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓒ [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ] [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ]

[ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ] [ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ]

( 1 , −1 ) ( 1 , −1 )

( −2 , 5 , 2 ) ( −2 , 5 , 2 )

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 1 2 z + 4 ; y = 1 2 z − 6 ; z x = 1 2 z + 4 ; y = 1 2 z − 6 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

Section 4.6 Exercises

ⓐ 6 ⓑ −14 −14 ⓒ −6 −6

ⓐ 9 ⓑ −3 −3 ⓒ 8

( 7 , 6 ) ( 7 , 6 )

( −9 , 3 ) ( −9 , 3 )

inconsistent

Section 4.7 Exercises

ⓐ false ⓑ true

ⓐ { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 ⓑ

ⓐ { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c ⓑ

ⓐ { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 ⓑ

ⓐ { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 ⓑ

Review Exercises

( 3 , −1 ) ( 3 , −1 )

one solution, consistent system, independent equations

( 3 , 1 ) ( 3 , 1 )

( 4 , −1 ) ( 4 , −1 )

elimination

50 irises and 150 tulips

10 calories jogging and 10 calories cycling

35 ° 35 ° and 55 ° 55 °

the length is 450 feet, the width is 264 feet

1 2 1 2 an hour

the rate of the jet is 395 mph, the rate of the wind is 7 mph

41 dimes and 11 pennies

46 2 3 46 2 3 liters of 30% solution, 23 1 3 23 1 3 liters of 60% solution

$29,000 for the federal loan, $14,000 for the private loan

( −3 , 2 , −4 ) ( −3 , 2 , −4 )

[ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ] [ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ]

{ x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3 { x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3

ⓐ [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] ⓑ [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] ⓒ [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ] [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ]

( −2 , 5 , −2 ) ( −2 , 5 , −2 )

ⓐ { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 ⓑ

Practice Test

( 2 , 1 ) ( 2 , 1 )

( 2 , −2 , 1 ) ( 2 , −2 , 1 )

15 liters of 1% solution, 5 liters of 5% solution

The candy cost $20; the cookies cost $5; and the popcorn cost $10.

ⓐ { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C ⓑ

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• Authors: Lynn Marecek
• Publisher/website: OpenStax
• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-4

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Chapter 1, Lesson 5: Solving Inequalities

• Extra Examples
• Personal Tutor
• Self-Check Quizzes

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Alg1.2 Linear Equations, Inequalities, and Systems

In this unit, students expand and deepen their prior understanding of expressions, equations, and inequalities. Students reason about equations, inequalities, and systems of equations and inequalities as ways to represent constraints, and they reason about the process of solving equations and inequalities in terms of finding values that satisfy those constraints. The process of finding solutions may involve rewriting and manipulating equations. Students learn to explain and validate the steps to do so. Throughout the unit, students practice reasoning about situations and mathematical representations, interpreting expressions and numbers in context, and using mathematical tools to model quantities and relationships.

Writing and Modeling with Equations

• 1 Planning a Pizza Party
• 2 Writing Equations to Model Relationships (Part 1)
• 3 Writing Equations to Model Relationships (Part 2)
• 4 Equations and Their Solutions
• 5 Equations and Their Graphs

Manipulating Equations and Understanding Their Structure

• 6 Equivalent Equations
• 7 Explaining Steps for Rewriting Equations
• 8 Which Variable to Solve for? (Part 1)
• 9 Which Variable to Solve for? (Part 2)
• 10 Connecting Equations to Graphs (Part 1)
• 11 Connecting Equations to Graphs (Part 2)

Systems of Linear Equations in Two Variables

• 12 Writing and Graphing Systems of Linear Equations
• 13 Solving Systems by Substitution
• 14 Solving Systems by Elimination (Part 1)
• 15 Solving Systems by Elimination (Part 2)
• 16 Solving Systems by Elimination (Part 3)
• 17 Systems of Linear Equations and Their Solutions

Linear Inequalities in One Variable

• 18 Representing Situations with Inequalities
• 19 Solutions to Inequalities in One Variable
• 20 Writing and Solving Inequalities in One Variable

Linear Inequalities in Two Variables

• 21 Graphing Linear Inequalities in Two Variables (Part 1)
• 22 Graphing Linear Inequalities in Two Variables (Part 2)
• 23 Solving Problems with Inequalities in Two Variables

Systems of Linear Inequalities in Two Variables

• 24 Solutions to Systems of Linear Inequalities in Two Variables
• 25 Solving Problems with Systems of Linear Inequalities in Two Variables
• 26 Modeling with Systems of Inequalities in Two Variables

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Unit 6 – Linear Equations and Inequalities

Solutions to Equations

LESSON/HOMEWORK

LECCIÓN/TAREA

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

SMART NOTEBOOK

Two-Step Equations

More Work with Two-Step Equations

Manipulating Expressions within Equations

Recognizing Structure to Solve Two-Step Equations

Solving Word Problems with Two-Step Equations Day 1

Solving Word Problems with Two-Step Equations Day 2

Solving Two-Step Inequalities

An Interesting Property of Inequalities

Modeling with Inequalities

Unit Review

Unit 6 Review

UNIT REVIEW

REPASO DE LA UNIDAD

EDITABLE REVIEW

Unit 6 Assessment Form A

EDITABLE ASSESSMENT

Unit 6 Assessment – Form B

Unit 6 Exit Tickets

Unit 6 Mid-Unit Quiz – Form A

Unit 6 Mid-Unit Quiz – Form B

U06.AO.01 – Practice Solving Two Step Equations

EDITABLE RESOURCE

U06.AO.02 – Practice with Modeling with Two-Step Equations

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Chapter 5, Lesson 3: Inequalities

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