Chapter 5 Worksheets - Commack Schools

NOMBRE5FECHAPERÍODOEjercicios preparatoriosDesigualdades linealesPaso 1Antes de comenzar el Capítulo 5 Lee cada enunciado. Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado. Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a)).PASO 1A, D o NSPASO 2AoDEnunciado1. Según la propiedad de adición de la desigualdad, sumarcualquier número a cada lado de una desigualdad verdaderadará como resultado una desigualdad verdadera.2. La desigualdad m 23 35 se puede resolver al sumar 23a cada lado.3. 16 no es más que la diferencia entre un número y 12 sepuede escribir como 16 n – 12.r4. Si ambos lados de 4 se multiplican por 12, el12resultado es r 48.5. El resultado de dividir ambos lados de la desigualdad–2y 10 entre –2 es y –5.7. Para resolver la desigualdad 8x – 2 70, primero divideentre 8 y luego suma 2.8. Una desigualdad compuesta es una desigualdad que contienemás de una variable.9. En una recta numérica, un punto cerrado se usa para unadesigualdad con el símbolo o .10. Si t 8, entonces t igual a todos los númerosentre 0 y 8.11. En la gráfica de y 2x – 3, el conjunto solución será el detodos los números arriba de la gráfica de la recta y 2x – 3.Paso 2Después de completar el Capítulo 5 Vuelve a leer cada enunciado y completa la última columna con una A o una D. ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna? En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.Capítulo 54Álgebra 1 de GlencoeCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Para resolver una desigualdad que implica multiplicación,como 9t 27, se usa la división.

NAMEDATE5-1PERIODStudy Guide and InterventionSolving Inequalities by Addition and SubtractionSolve Inequalities by Addition Addition can be used to solve inequalities. If anynumber is added to each side of a true inequality, the resulting inequality is also true.Addition Property of InequalitiesFor all numbers a, b, and c, if a b, then a c b c,and if a b, then a c b c.Example 2Solve 4 - 2a -a. Thengraph the solution.4 - 2a -aOriginal inequality4 - 2a 2a -a 2a Add 2a to each side.4 aSimplify.a 44 a is the same as a 4.Example 1Solve x - 8 -6.Then graph the solution.x - 8 -6Original inequalityx - 8 8 -6 8 Add 8 to each side.x 2Simplify.The solution in set-builder notation is{x x 2}.Number line graph:-4 -3 -2 -10123The solution in set-builder notation is {a a 4}.Number line graph:4-2 -10123456ExercisesCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Solve each inequality. Check your solution, and then graph it on a number line.1. t - 12 1626 27 28 29 30 31 32 33 344. n - 8 -13-10 -9 -8 -7 -6 -5 -4 -3 -22. n - 12 63. 6 g - 312 13 14 15 16 17 18 19 205. -12 -12 y-4 -3 -2 -1 01789 10 11 12 13 14 156. -6 m - 8234-4 -3 -2 -1 01234Solve each inequality. Check your solution.7. -3x 8 - 4x10. -y - 10 15 - 2y8. 0.6n 12 - 0.4n1411. z - 39. -8k - 12 - 9k12. -2b -4 - 3b3Define a variable, write an inequality, and solve each problem. Checkyour solution.13. A number decreased by 4 is less than 14.14. The difference of two numbers is more than 12, and one of the numbers is 3.15. Forty is no greater than the difference of a number and 2.Chapter 55Glencoe Algebra 1Lesson 5-1The property is also true when and are replaced with and .

NAME5-1DATEPERIODStudy Guide and Intervention(continued)Solving Inequalities by Addition and SubtractionSolve Inequalities by SubtractionSubtraction can be used to solve inequalities. If anynumber is subtracted from each side of a true inequality, the resulting inequality is also true.Subtraction Property of InequalitiesFor all numbers a, b, and c, if a b, then a - c b - c,and if a b, then a - c b - c.The property is also true when and are replaced with and .ExampleSolve 3a 5 4 2a. Then graph it on a number line.3a 5 4 2a3a 5 - 2a 4 2a - 2aa 5 4a 5-5 4-5a -1The solution is {a a -1}.Number line graph:Original inequalitySubtract 2a from each side.Simplify.Subtract 5 from each side.Simplify.-4 -3 -2 -1Exercises01234Solve each inequality. Check your solution, and then graph it on a number line.1. t 12 82. n 12 -123. 16 h 9124. y 4 - 2-8 -7 -6 -5 -4 -3 -2 -1 05-26 -25 -24 -23 -22 -21234256789Solve each inequality. Check your solution.317. 4p 3p 0.78. r 410. -1.2 2.4 y789 10 11 12 13316. q-5 q5. 3r 6 4r16811. 4y 5y 1420123456789. 9k 12 8k12. 3n 17 4nDefine a variable, write an inequality, and solve each problem. Check yoursolution.13. The sum of a number and 8 is less than 12.14. The sum of two numbers is at most 6, and one of the numbers is -2.15. The sum of a number and 6 is greater than or equal to -4.Chapter 56Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.-6 -5 -4 -3 -2 -1 0

NAMEDATE5-1PERIODSkills PracticeSolving Inequalities by Addition and SubtractionMatch each inequality to the graph of its solution.a.2. x - 6 1b.3. x 2 -3c.4. x 3 1d.5. x - 1 -7e.-8 -7 -6 -5 -4 -3 -2 -1 0-4 -3 -2 -1 00123412345678Lesson 5-11. x 11 16-8 -7 -6 -5 -4 -3 -2 -1 0012345678Solve each inequality. Check your solution, and then graph it on a number line.6. d - 5 10127. t 9 8345678Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8. a - 7 -13-4 -3 -2 -1 023456789. w - 1 40-8 -7 -6 -5 -4 -3 -2 -1 010. 4 k 3-4 -3 -2 -1 01123411. -9 b - 4123412. -2 x 4-8 -7 -6 -5 -4 -3 -2 -1 013. 2y y 2-8 -7 -6 -5 -4 -3 -2 -1 0-4 -3 -2 -1 01234Define a variable, write an inequality, and solve each problem.Check your solution.14. A number decreased by 10 is greater than -5.15. A number increased by 1 is less than 9.16. Seven more than a number is less than or equal to -18.17. Twenty less than a number is at least 15.18. A number plus 2 is at most 1.Chapter 57Glencoe Algebra 1

NAME5-1DATEPERIODPracticeSolving Inequalities by Addition and SubtractionMatch each inequality with its corresponding graph.1. -8 x - 15a.2. 4x 3 5xb.3. 8x 7x - 4c.4. 12 x 9d.-6 -5 -4 -3 -2 -1 001234561278-8 -7 -6 -5 -4 -3 -2 -1 0012345678Solve each inequality. Check your solution, and then graph it on a number line.6. 3x 8 4x5. r - (-5) -2-8 -7 -6 -5 -4 -3 -2 -1 07. n - 2.5 -5-4 -3 -2 -1 03456789 10-4 -3 -2 -1 0123412348. 1.5 y 112343110. c- 29. z 3 3-4 -3 -2 -1 0221234-4 -3 -2 -1 0411. The sum of a number and 17 is no less than 26.12. Twice a number minus 4 is less than three times the number.13. Twelve is at most a number decreased by 7.14. Eight plus four times a number is greater than five times the number.15. ATMOSPHERIC SCIENCE The troposphere extends from the Earth’s surface to a heightof 6–12 miles, depending on the location and the season. If a plane is flying at analtitude of 5.8 miles, and the troposphere is 8.6 miles deep in that area, how muchhigher can the plane go without leaving the troposphere?16. EARTH SCIENCE Mature soil is composed of three layers, the uppermost being topsoil.Jamal is planting a bush that needs a hole 18 centimeters deep for the roots. Theinstructions suggest an additional 8 centimeters depth for a cushion. If Jamal wants toadd even more cushion, and the topsoil in his yard is 30 centimeters deep, how muchmore cushion can he add and still remain in the topsoil layer?Chapter 58Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Define a variable, write an inequality, and solve each problem. Checkyour solution.

NAME5-1DATEPERIODWord Problem PracticeSolving Inequalities by Addition and Subtraction5. WEATHER Theodore Fujita of theUniversity of Chicago developed aclassification of tornadoes according towind speed and damage. The table showsthe classification system.2. GARBAGE The amount of garbage thatthe average American adds to a landfilldaily is 4.6 pounds. If at least 2.5 poundsof a person’s daily garbage could berecycled, how much will still go intoa landfill?LevelNameWind Speed yright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Source: National Weather Servicea. Suppose an F3 tornado has winds thatare 162 miles per hour. Write andsolve an inequality to determine howmuch the winds would have toincrease before the F3 tornadobecomes an F4 tornado.3. SHOPPING Tyler has 75 to spend atthe mall. He purchases a music video for 14.99 and a pair of jeans for 18.99. Healso spent 4.75 for lunch. Tyler stillwants to purchase a video game. Howmuch money can he spend on a videogame?b. A tornado has wind speeds that are atleast 158 miles per hour. Write andsolve an inequality that describes howmuch greater these wind speeds arethan the slowest tornado.4. SUPREME COURT The first ChiefJustice of the U.S. Supreme Court, JohnJay, served 2079 days as Chief Justice.He served 10,463 days fewer than JohnMarshall, who served as Supreme CourtChief Justice for the longest period oftime. How many days must the currentSupreme Court Chief Justice JohnRoberts serve to surpass John Marshall’srecord of service?Chapter 59Glencoe Algebra 1Lesson 5-11. SOUND The loudest insect on Earth isthe African cicada. It produces sounds asloud as 105 decibels at 20 inches away.The blue whale is the loudest mammalon Earth. The call of the blue whale canreach levels up to 83 decibels louder thanthe African cicada. How loud are thecalls of the blue whale?

NAME5-1DATEPERIODEnrichmentTriangle InequalitiesRecall that a line segment can be named by the letters of its endpoints. Line segment AB (written as AB) has points A and B forendpoints. The length of AB is written without the bar as AB.AB BCm A m B The statement on the left above shows that AB is shorter than BC.The statement on the right above shows that the measure of angle Ais less than that of angle B.These three inequalities are true for any triangle ABC,no matter how long the sides.a. AB BC ACb. If AB AC, then m C m B.c. If m C m B, then AB AC.BACUse the three triangle inequalities for these problems.1. List the sides of triangle DEF in order of increasing length.D85 35 60 EK65 J50 55 65 60 L65 M3. Explain why the lengths 5 centimeters, 10 centimeters, and20 centimeters could not be used to make a triangle.4. Two sides of a triangle measure 3 inches and 7 inches. Between which twovalues must the third side be?5. In triangle XYZ, XY 15, YZ 12, and XZ 9. Which angle has thegreatest measure? Which has the least?6. List the angles A, C, ABC, and ABD, in order of increasing size.C13B12155D9AChapter 510Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.F2. In the figure at the right, which line segment is the shortest?

NAMEDATE5-2PERIODStudy Guide and InterventionSolving Inequalities by Multiplication and DivisionSolve Inequalities by MultiplicationIf each side of an inequality is multiplied bythe same positive number, the resulting inequality is also true. However, if each side of aninequality is multiplied by the same negative number, the direction of the inequality mustbe reversed for the resulting inequality to be true.For all numbers a, b, and c, with c 0,1. ifif2. ififMultiplication Property of Inequalitiesccccisisisispositive and a b, then ac bc;positive and a b, then ac bc;negative and a b, then ac bc;negative and a b, then ac bc.The property is also true when and are replaced with and .y8y- 128( 8y )(-8) - (-8)12y -9643k 15 4Original inequalityMultiply each side by -8; change to .Original inequality( 43 ) 34 k ( 43 )15k 20Simplify.The solution is { y y -96}.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3Solve k 15.Example 2Solve - 12.4Multiply each side by .3Simplify.The solution is {k k 20}.ExercisesSolve each inequality. Check your solution.y6p61. 2n2. - 2233. h -34. - -615. n 10126. - b 3m37. - 2h8. -2.51 - 4g59. -2503359p310. - - 455n11. 5.4102042a12. -67Define a variable, write an inequality, and solve each problem. Checkyour solution.13. Half of a number is at least 14.14. The opposite of one-third a number is greater than 9.15. One fifth of a number is at most 30.Chapter 511Glencoe Algebra 1Lesson 5-2Example 1

NAMEDATE5-2Study Guide and InterventionPERIOD(continued)Solving Inequalities by Multiplication and DivisionSolve Inequalities by Division If each side of a true inequality is divided by thesame positive number, the resulting inequality is also true. However, if each side of aninequality is divided by the same negative number, the direction of the inequality symbolmust be reversed for the resulting inequality to be true.For all numbers a, b, and c with c 0,Division Propertyof Inequalitiesabab1. if c is positive and a b, then c c ; if c is positive and a b, then c c;abab2. if c is negative and a b, then c c ; if c is negative and a b, then c c.The property is also true when and are replaced with and .ExampleSolve -12y 48.-12y 48Original inequality-12y48 Divide each side by -12 and change to .-12-12y -4Simplify.The solution is { y y -4}.ExercisesSolve each inequality. Check your solution.2. -2x 93. -5c 24. -8m -6415. -6k 6. 18 -3b7. 30 -3n8. -0.24 0.6w10. -30 -5p11. -2n 6.2214. - 615. -3 59. 25 -2m13. -40 10h3np412. 35 0.05h-x16. 4 2Define a variable, write an inequality, and solve each problem. Then checkyour solution.17. Four times a number is no more than 108.18. The opposite of three times a number is greater than 12.19. Negative five times a number is at most 100.Chapter 512Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1. 25g -100

NAMEDATE5-2PERIODSkills PracticeSolving Inequalities by Multiplication and Division1. 3n 9a. Three times a number is at most nine.12. n 9b. One third of a number is no more than nine.3. 3n 9c. Negative three times a number is more than nine.4. -3n 9d. Three times a number is less than nine.15. n 9e. Negative three times a number is at least nine.6. -3n 9f. One third of a number is greater than or equal to nine.33Solve each inequality. Check your solution.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. 14g 568. 11w 779. 20b -12010. -8r 16p711. -15p -90x12. 9a13. -1514. - -9t15. - 616. 5z -9017. -13m -26k18. -1719. -y 3620. -16c -224h21. - 2d22. 12 124910512Define a variable, write an inequality, and solve each problem.Check your solution.23. Four times a number is greater than -48.24. One eighth of a number is less than or equal to 3.25. Negative twelve times a number is no more than 84.26. Negative one sixth of a number is less than -9.27. Eight times a number is at least 16.Chapter 513Glencoe Algebra 1Lesson 5-2Match each inequality with its corresponding statement.

NAMEDATE5-2PERIODPracticeSolving Inequalities by Multiplication and DivisionMatch each inequality with its corresponding statement.1. -4n 5a. Negative four times a number is less than five.4n 52. b. Four fifths of a number is no more than five.3. 4n 5c. Four times a number is fewer than five.4n 54. d. Negative four times a number is no less than five.5. 4n 5e. Four times a number is at most five.6. -4n 5f. Four fifths of a number is more than five.55Solve each inequality. Check your solution.a -147. - 58. -13h 52b9. -61610. 39 13p211. n -12512. - t 25313. - m -61014. k -1015. -3b 0.7516. -0.9c -917. 0.1x -418. -2.3 19. -15y 320. 2.6v -20.821. 0 -0.5u722. f -139538Define a variable, write an inequality, and solve each problem. Checkyour solution.23. Negative three times a number is at least 57.24. Two thirds of a number is no more than -10.25. Negative three fifths of a number is less than -6.26. FLOODING A river is rising at a rate of 3 inches per hour. If the river rises more than2 feet, it will exceed flood stage. How long can the river rise at this rate withoutexceeding flood stage?27. SALES Pet Supplies makes a profit of 5.50 per bag on its line of natural dog food. If thestore wants to make a profit of no less than 5225 on natural dog food, how many bagsof dog food does it need to sell?Chapter 514Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.j4

NAME5-2DATEPERIODWord Problem PracticeSolving Inequalities by Multiplication and Division4. EVENT PLANNING The DowntownCommunity Center does not charge arental fee as long as a rentee orders aminimum of 5000 worth of food fromthe center. Antonio is planning a banquetfor the Quarterback Club. If he isexpecting 225 people to attend, what isthe minimum he will have to spend onfood per person to avoid paying a rentalfee?5. PHYSICS The density of a substancedetermines whether it will float orsink in a liquid. The density of water is1 gram per milliliter. Any object with agreater density will sink and any objectwith a lesser density will float. Densitymis given by the formula d v , wherem is mass and v is volume. Here is atable of common chemical solutions andtheir densities.Copyright Glencoe/McGraw-Hill, a divisi

materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com. Chapter Resources Student-Built Glossar