Holt California Algebra 1
Holt CaliforniaAlgebra 1Review for Mastery WorkbookTeacher’s Guide
Copyright by Holt, Rinehart and WinstonAll rights reserved. No part of this publication may be reproduced or transmitted in any form or byany means, electronic or mechanical, including photocopy, recording, or any information storageand retrieval system, without permission in writing from the publisher.Teachers using the HOLT CALIFORNIA ALGEBRA 1 may photocopy complete pages in sufficientquantities for classroom use only and not for resale.HOLT and the “Owl Design” are trademarks licensed to Holt, Rinehart and Winston, registered inthe United States of America and/or other jurisdictions.Printed in the United States of AmericaIf you have received these materials as examination copies free of charge, Holt, Rinehart andWinston retains title to the materials and they may not be resold. Resale of examinationcopies is strictly prohibited.Possession of this publication in print format does not entitle users to convert this publication,or any portion of it, into electronic format.ISBN 978-0-03-094693-6ISBN 0-03-094693-x1 2 3 4 5 6 7 8 9 862 10 09 08 07
ContentsChapter 1 .1Chapter 2 .4Chapter 3 .8Chapter 4 .11Chapter 5 .14Chapter 6 .17Chapter 7 .21Chapter 8 .25Chapter 9 .28Chapter 10 .33Chapter 11 .37Copyright by Holt, Rinehart and Winston.All rights reserved.iiiHolt Algebra 1
NameCalifornia Standards Prep forDateClassNameCalifornia Standards Prep for4.0Review for Mastery1-1 Variables and ExpressionsLESSONTo translate words into algebraic expressions, find words likethese that tell you the operation. esincreaseddecreasedper 9 when 20 is placed in the box.Evaluate 920 911In algebra, variables are used instead of boxes.Evaluate x 7 for x 28.v represents the number of video games Kenny owns.x 7v 7Think: The word “more” indicates addition.Order does not matter for addition. The expression 7 v is also correct.28 74Jenny is 12 years younger than Candy. Write an expression for Jenny’s ageif Candy is c years old.c represents Candy’s age.Sometimes, the expression has more than one variable.Evaluate x y for x 6 and y 2.The word “younger” means “less,” which indicates subtraction.x yThink: Candy is older, so subtract 12 from her age.6 2Order does matter for subtraction. The expression 12 c is incorrect.81. Jared can type 35 words per minute. Writean expression for the number of words hecan type in m minutes.Evaluate 5 35mh 0.57. 58. 241011. 15 z10. 3y1819c 254. Enrique collected 152 recyclable bottles, andLatasha collected b recyclable bottles. Writean expression for the number of bottles theycollected altogether.29Evaluate each expression for x 4, y 6, and z 3.9. x 153. Mrs. Knighten bought a box of c crayons andsplit them evenly between the 25 students inher classroom. Write an expression for thenumber of crayons each student received.12Evaluate each expression for x 2, y 18, and z 9.13. y x12. x · z152 b5. Tammy’s current rent is r dollars. Next month itwill be reduced by 50. Write an expression fornext month’s rent in dollars.01-14 RevMastWB CA.indd 1when each number is placed in the box.6. 382. Mr. O’Brien’s commute to work is 0.5 hourless than Miss Santos’s commute. Write anexpression for the length of Mr. O’Brien’scommute if Miss Santos’s commute is h hours.NameCalifornia Standards 9 depends on what number is placed in the box.The value of dividequotientsplitratioKenny owns v video games. Stan owns 7 more video games than Kenny.Write an expression for the number of video games Stan owns.y15.x36ClassNameCalifornia StandardsReview for Mastery1-2 Adding and Subtracting Real Numbers72Copyright by Holt, Rinehart and Winston.All rights reserved.2.0217. z x16. xy9Holt Algebra 1Date14. y z1618r 501Copyright by Holt, Rinehart and Winston.All rights reserved.ClassReview for Mastery1-1 Variables and Expressions continuedLESSONc 12Date4.0Holt Algebra 1DateClass2.0Review for Mastery1-2 Adding and Subtracting Real Numbers continued12/29/06 5:39:4401-14 RevMastWB CA.inddPM2LESSONLESSON12/29/06 5:39:45 PMThese rules apply to the addition of all real numbers, not just integers:You can model integer addition using two-color counters. Use the yellowside for 1 and the red side for –1. A yellow counter and a red counter areopposites, so they sum to 0 and cancel.To Add Numbers with the Same SignAdd the numbers’ absolute values and use the same sign as the numbers.Add 4 6.To Add Numbers with Different SignsRRRRYYYYFind the difference of the numbers’ absolute values and use the sign of thenumber with the greater absolute value. 2 4 6 YY Add 1 3 .55Use the rule for adding numbers with the same sign.To subtract integers using counters, remember that subtracting a numberis the same as adding the opposite of the number.Subtract 5 8. 1 155To subtract 8, add 8.55 8 5 ( 8) YYYYYRRRRRRR 3R 31. 2 ( 5) YRRR2. 4 ( 1) R5Find the absolute values.Add the absolute values.5 Both addends are negative, so the result is negative.Subtract 2.9 ( 3.5).YR 3 355Use the same sign as the numbers. 1 3 4555Add or subtract by drawing a model of two-color counters.Yand1 3 4YY5Change subtraction to addition.YUse the rule for adding numbers with different signs. 2.9 3.5YAdd or subtract using two color counters.To subtract 3.5, add 3.5. 2.9 2.9 and 3.5 3.5Find the absolute values.3.5 2.9 0.6Find the difference.Use the sign of the number with the greater absolute value.3. 3 74. 3 ( 4) 2.9 ( 3.5) 0.65. 2 6 8 143.5 had the greater absolute value in the additionproblem, so the result is positive.Add or subtract.6. 8 27. 5 3 869. 6 ( 4)8. 7 ( 4)10. 5 ( 5)03Copyright by Holt, Rinehart and Winston.All rights reserved.01-14 RevMastWB CA.indd 313. 6.5 ( 3.2) 415. 12 ( 15)11. 2 7 2Copyright by Holt, Rinehart and Winston.All rights reserved.12. 5 ( 9)11 53Holt Algebra 1Copyright by Holt, Rinehart and Winston.All rights reserved.112/29/06 5:39:4501-14 RevMastWB CA.inddPM414. 5 199 9.716. 7.8 2.5 10.3417. 3 588 49 2 148Holt Algebra 1Holt Algebra 112/29/06 5:39:46 PM
NameCalifornia StandardsDateClassNameCalifornia Standards2.0Review for Mastery1-3 Multiplying and Dividing Real NumbersLESSONTo multiply or divide real numbers, first use the rules below to determine the sign of the result.Then operate with the numbers as if they have no signs.( )( )( )( )···· ( )( )( )( )Division( )( )( )( )( )( )( )( ) To multiply by a fraction, you multiply the numerators and multiply the denominators.To divide by a fraction, you multiply by the reciprocal. Two numbers are reciprocalsif their product is 1.In General( )( )( )( ) 40 1.For example, 5 and 8 are reciprocals because 5 8 858 540When you multiply or divide fractions that are signed numbers, you apply the samerules as for any real number: same sign ( ) and different signs ( ).Divide 3 3 .45same sign ( )different signs ( )different signs ( )same sign ( )( )( )( )( ) Multiply –5 3. 5 3 5 3 3 Different signs mean the product is negative.4 5 3Multiply the numbers as if they have no signs. 15Multiply.Divide the fractions as if they have no signs. 3 54 3To divide by 3 multiply by the reciprocal 5 .5315 12Multiply the numerators and multiply the denominators.Same signs mean the quotient is positive. 2 0.5Divide the numbers as if they have no signs. 5Reduce. 4Divide.Divide 2 ( 0.5). 2 ( 0.5) 4 4Use a reciprocal to write an equivalent multiplication expression.Determine the sign ( or –) for each product or quotient. 2. 156 ( 8) 19.5 1. 8 4 32 6.4 ( 4) 1.65. 0.5(0.4) 0.2 3. 15(4) 606.7. 3 78. 55 11 21 2414. 8.2 5 5.117. 4.5 1.5 5 DateClassNameCalifornia Standards Prep for14Holt Algebra 1DateClass2.0Review for Mastery1-4 Powers and Exponents continued12/29/06 5:39:47 PMLESSONSome numbers can be written as a power of a given base. For example, 8 is a power3of 2 because 2 8.If you know that a number is a power of a given base, you can find the exponent bydoing repeated multiplication.Write 81 as a power of 3.PowerBaseExponent54545 5 5 5 5454 (5 5 5 5) 54( 5) ( 5) ( 5) ( 5)Expanded Form 3 ( 3) 1( 3)( 3) 9 ( 3) 2( 3)( 3)( 3) 27 ( 3) 3( 3)( 3)( 3)( 3) 81 ( 3) 481 ( 3) 4 45 .3There are parentheses, so the exponent influences the negative and the fraction.Complete each table. 45 11. powers of 2 45 45 45 16 4 Multiply two of the factors. A negative times a negative is positive.25 5 64 125Multiply again. A positive times a negative is negative.7 7 7 7 7 76211 1 1 1 1 1 1222222( 3) ( 3)2. ( 3) 24. 62512. powers of 3Power Multiplication ValueWrite the expanded form of each power.73. 12 112/29/06 5:39:4601-14 RevMastWB CA.inddPM6To evaluate a power, perform the repeated multiplication.1. 7 6Copyright by Holt, Rinehart and Winston.All rights reserved.A power is an expression that represents repeated multiplication of a factor.The factor is the base, and the number of times it is used as a factor is theexponent. Pay attention to parentheses, which tell you how much of theexpression the exponent influences.3 2130. 1 2 1631 2752.0Review for Mastery1-4 Powers and ExponentsEvaluate 429. 2 ( 6)98Holt Algebra 1LESSON( 5)27. 7 13 5.13Copyright by Holt, Rinehart and Winston.All rights reserved.47 18416 18. 3.4 ( 1.5) 10.8NameCalifornia Standards Prep for 724. 5 910 2528. 5 64818 61or 18 621. 18 1 6126. 4 155 2.14116. 2.7(4) 915. 21 10223. 3 28325. 3 283 2.54813. 15.3 386412. 5 ( 2) 543 320. 3 2 8315 9. 6( 4)11. 6( 8)5Multiply or divide.22. 3 58 8 29.82 2.1 14.2510. 100 202 919. 2 4 59Multiply or divide.01-14 RevMastWB CA.indd 5Different signs mean the quotient is negative. 3 345 154.ClassReview for Mastery1-3 Multiplying and Dividing Real Numbers continuedLESSONMultiplicationDate2.02213. powers of 10Power Multiplication ValuePower MultiplicationValue313310 13·39103·3·32710 310 · 10 · 10100010,0001010 · 38110 410 · 10 · 10 · 10252·2·2·2·232353·3·3·3·324310 510 · 10 · 10 · 10 · 10 100,0003210 (6 6 6 6 6)Write each number as a power of the given base.Evaluate each expression.5. 36. 258. ( 2)7. 9 29. 1814. 16; base 2228217Copyright by Holt, Rinehart and Winston.All rights reserved.01-14 RevMastWB CA.indd 7Holt Algebra 14Copyright by Holt, Rinehart and Winston.All rights reserved.212/29/06 5:39:4701-14 RevMastWB CA.inddPM819. 10,000; base 100( 3) 7( 4)810022. 1 ; base 18205Copyright by Holt, Rinehart and Winston.All rights reserved.10 621. 4096; base 420. 625; base 5 816. 1,000,000; base 103318. 2187; base 317. 256; base 28110. 015. 27; base 3244 16243346 12 23Holt Algebra 1Holt Algebra 112/29/06 5:39:48 PM
NameCalifornia StandardsDateClassNameCalifornia Standards2.0Review for Mastery1-5 Roots and Irrational NumbersDateClass2.0Review for Mastery1-5 Roots and Irrational Numbers continuedLESSONLESSONThe square root of a number is the positive factor that you would square to getthat number.Real Numbersthe square root of 9 is 3 because 3 squared is 9 Rational Numbers 9 3 because 3 3 3 92This flowchart shows thesubsets of the real numbersand how they are related.To identify the classifications ofa real number, start at thetop and work your way down.A negative square root is the negative factor that you would square to get the number.the negative square root of 25 is –5 because –5 squared is 25 25 5 because ( 5) 2 ( 5)( 5) 25To evaluate a square root, think in reverse. Ask yourself, “What number do I square?”Terminating DecimalsIrrational NumbersRepeating DecimalsNon-IntegersIntegersNegative Integers Whole NumbersFind 36.( 6) 2 ( 6)( 6) 36ZeroThink: What negative factor do you square to get 36?Natural Numbers 36 6 Find. 814Think about the numerator and denominator separately.22 49 81 9 22 4 can be shown on a number line. It is real.Think: What number do I square to get 81? 9 29 4 81Write all of the classifications that apply to the real number –4.Think: What number do I square to get 4?242 812Its decimal representationterminates: 4 4.0.9121243249216526252362. Complete this table of square roots.7249 4 9 16 25 36 491234567 96422108111212213121 144 169100 64 81 100 121 8109 6. 40011 20 1691312 8113 4. 64 1169 5. 256 258. 1449Copyright by Holt, Rinehart and Winston.All rights reserved.NameCalifornia Standards 1.0, 24.3, 25.11610. 135 11. 5Whole NumbersZeroNatural Numbersreal number, rational number, terminating decimal, integer,whole number, natural numberreal number, rational number, repeating decimal 12Holt Algebra 1Date10Holt Algebra 1NameCalifornia Standards 1.0, 24.3, 25.1DateClassReview for Mastery1-6 Properties of Real Numbers continued12/29/06 5:39:4801-14 RevMastWB CA.inddPM10LESSON12/29/06 5:39:49 PMLESSONThe following properties make it easier to do mental math.A set of numbers has closure under an operation if the result of the operation on any twonumbers in the set is also in the set.PropertyAdditionMultiplicationCommutative Property3 4 4 32 5 5 2Associative Property(3 4) 5 3 (4 5)(2 4) 10 2 (4 10)The integers are closed under addition, subtraction, and multiplication.Operation2(5 9) 2(5) 2(9)Distributive Propertyreal number, irrational numberCopyright by Holt, Rinehart and Winston.All rights reserved.ClassReview for Mastery1-6 Properties of Real Numbers01-14 RevMastWB CA.indd 9Negative IntegersWrite all classifications that apply to each real number.9. 247.Integers 14411Find each square root.3. 121Non-Integers 4 is a negative integer. Stop.There are no more subsets in thechart below negative integers.2Irrational NumbersRepeating Decimals 4: real number, rational number, terminating decimal, integer 1 82Rational NumbersTerminating Decimals 4 is an integer.1. Complete this table of squares.2Real Numbers 4 can be written as 4 so it is rational.1Combine the numerator and denominator to form a positive factor.The Commutative Property shows the same numbers rearranged in differentways, so 17 makes the statement true.Algebra5 9 14For integers a and b, a bis an integer.Subtraction12 20 8For integers a and b, a bis an integer.Multiplication4 3 12For integers a and b, ab isan integer.Determine the number that makes the statement true.15 17 15 illustrates the Commutative Property.NumbersAdditionA counterexample is an example that proves a statement false. 4 t 4 t 23 illustrates the Associative Property.Find a counterexample to disprove the statement “The natural numbers are closedunder subtraction.”The Associative Property shows the same numbers grouped in different ways,so 23 makes the statement true.Find two natural numbers, a and b, such that their difference is not a natural number.a b 4 9 5Since 5 is not a natural number, this is a counterexample. The statement is false.3 ( x) 3(10) 3(x) illustrates the Distributive Property.The Distributive Property says that when multiplying a number by a sum, you canmultiply by each number in the sum and then add, so 10 makes the statement true.Find a counterexample to show that each statement is false.7. The whole numbers are closed under division.Determine the number that makes the statement true.Possible answer: 5 2 2.536 36 13 illustrates the Commutative Property.1. 13 7 illustrates the Associative Property.2. 21 5 7 21 5 8. The set of negative integers is closed under subtraction.20 8 12 20 12 8 illustrates the Distributive Property.3. 12 Possible answer: 2 3 12 11 31 2 illustrates the Associative Property.4. 11 31 22 illustrates the Commutative Property.5. 22 8 8 9. The rational numbers are closed under the operation of taking a square root. Possible answer: 24 illustrates the Distributive Property.6. 6 30 4 6 30 6( )Copyright by Holt, Rinehart and Winston.All rights reserved.11Copyright by Holt, Rinehart and Winston.All rights reserved.01-14 RevMastWB CA.indd 11Holt Algebra 1Copyright by Holt, Rinehart and Winston.All rights reserved.312/29/06 5:39:4901-14 RevMastWB CA.inddPM1212Holt Algebra 1Holt Algebra 112/29/06 5:39:50 PM
NameCalifornia Standards 1.1, 25.1DateClassNameCalifornia Standards 1.1, 25.1Review for Mastery1-7 Simplifying ExpressionsLESSONExpressions can contain more than one operation, and then can also include groupingsymbols, like parentheses ( ), brackets [ ], and braces { }. Operations must be performedin a certain order.I. Perform operations inside grouping symbols, with the innermost group being done first.II. Evaluate powers (exponents).III. Perform multiplication and division in order from left to right.IV. Perform addition and subtraction in order from left to right.Terms can be combined only if they are like terms. Like terms can have different coefficients,but they must have the same variables raised to the same powers.Like Terms24x , 7xSimplify the expression 6 3(5 1) 2.26 2 3(5 1) 2Evaluate 6 .26Simplify each expression.2. 18 3 2 5 2st 4, 3s 4tDistribute 4.4x 5x 4y 9Use the Commutative Property.9x 4y 9Add the like terms 4x and 5x.9x 4y 9No other terms are like terms.97yesnoSimplify each expression.2 3 2 4 3 58.26 22noIf possible, simplify each expression by combining like terms.3014. 10y 3 5y 4y 313. 7st 3st7. 2 6 (8 5) 212. 10a and 10b11. 2s 2 and 5s10. 4xy and 3xy6. 6 10 2 5 1274x 4y 5x 9State whether each pair of terms are like terms.145. 7 4 32Subtract the coefficients only.3. 3 5 3 8 2 194. 3 3 3 35ab 2, ab 2Simplify 4(x y) 5x 9.Add and subtract from left to right.1. 6 2 4 3312y, 12xy20x 3Evaluate 3 4.24 23m, 5m12y, 18y24x 3 4x 3236 12 2Not Like Terms2Simplify 24x 3 4x 3.Evaluate 5 1.36 3 4 2ClassReview for Mastery1-7 Simplifying Expressions continuedLESSON62 3 4 2Date336y 5y4st9. 4 3 2 6 5 15. 12x 3 6x 412x 6x4Simplify each expression.16. 3 x 6 2133013Copyright by Holt, Rinehart and Winston.All rights reserved.NameCalifornia Standards Prep for01-14 RevMastWB CA.indd 1316Holt Algebra 1Date5.0;Classx 4 10 4 4x 5 x 8Check:Solve equations involving multiplication and division byperforming the inverse operation.Solve x 4.5x 4 10?6 4 10?10 10x 4 812/29/06 5:39:50 PM5 x 4 55Check:Rewrite subtraction as addition.5x 20 5 x 8? 5 3 8? 5 5x 4Check:5?20 4x is divided by 5.5Add 4 to each side.5?4 4Multiply both sides by 5.Simplify.5x 20The opposite of 8 is 8. 8Class2.0Review for Mastery2-1 Solving One-Step Equations continuedThe opposite of 4 is 4.Find the oppositeof this number.Date5.0;LESSON6Solve 5 x 8.Holt Algebra 112/29/06 5:39:5001-14 RevMastWB CA.inddPM14Any addition equation can be solved by adding the opposite. If the equation involvessubtraction, it helps to first rewrite the subtraction as addition.Find the oppositeof this number.14NameCalifornia Standards Prep forReview for Mastery2-1 Solving One-Step Equations7y 2 y 5 y10y 10Copyright by Holt, Rinehart and Winston.All rights reserved.2.0LESSONSolve x 4 10.17.3x 16Solve 3x 27.Add 8 to each side. 3x 273 x 3x 27Check:? 3( 9) 27x is multiplied by 3.? 3x 27 3Rewrite each equation with addition. Then state the number thatshould be added to each side.1. x 7 122. x 8 5x 7 12; 7x 8 5; 3 3x 927 27Divide both sides by 3.Simplify.3. 4 x 2Circle the correct word in each sentence. Then solve the equation.x 710.11. 5m 40 2 4 x 2; 2x is multiplied/divided by 2.m is multiplied/divided by 5.To solve, multiply/divide both sides by 2.To solve, multiply/divide both sides by 5.Solve each equation. Check your answers.4. x 4 125. 21 x 287. x 10 6 166. x 3 8198. 8 x 2 6 14x 59. x 5 2Solve each equation. Check your answers.12. 2x 2013. w 75 710Copyright by Holt, Rinehart and Winston.All rights reserved.15Copyright by Holt, Rinehart and Winston.All rights reserved.15-28 RevMastWB CA.indd 15m Holt Algebra 1Copyright by Holt, Rinehart and Winston.All rights reserved.412/29/06 5:41:5115-28 RevMastWB CA.inddPM16 814. 6z 42 3516 7Holt Algebra 1Holt Algebra 112/29/06 5:41:52 PM
NameCalifornia Standards Prep forDateClassNameCalifornia Standards Prep for5.0Review for Mastery2-2 Solving Two-Step EquationsReview for Mastery2-2 Solving Two-Step EquationsLESSON4x 3 15x 2 93This will clear the fractions.Solve x 2 2.43x 2 243Multiply both sides by the LCD 12.12 x 2 12 23412 x 12 2 12 2 43Solve using Inverse Operations Add 3 to both sides. Then 3 is subtracted. Then divide both sides by 4. x is divided by 3. Add 2 to both sides. Then 2 is added. Then multiply both sides by 3. The order of the inverse operations is the order of operations in reverse.Check:5x 7 13x is multiplied by 5. Then 7 is subtracted. 7Add 7 to both sides.5x 205x20 55x 4 x is multiplied by 3. 8 is added. 8Add 8 to both sides.5x 7 13 83x16 316x 3413 134 b2. 4 26234 316 2 ? 21234? 2 2 336 ? 23 ? 22 Solve each equation. Check your answers.316. w 2 5. x 1283515Solve each equation. Check your answers. 2 2316 2 ? 213 Divide both sides by 3.3?4x1 x 2 23x 16? 1320 7 1. 3x 8 4Check: 3x 8 24? 135(4) 7 Divide both sides by 5.continuedA two-step equation with fractions can be simplified by multiplying each side by the LCD. x is multiplied by 4.Solve 5x 7 13. 7ClassLESSONWhen solving two-step equations, first identify the operations and the order in whichthey are applied to the variable. Then use inverse operations.OperationsDate5.0a7. 3 152603. 3y 4 94. 14 3x 1525 14255317Copyright by Holt, Rinehart and Winston.All rights reserved.NameCalifornia Standards15-28 RevMastWB CA.indd 17Holt Algebra 1Date4.0,ClassNameCalifornia Standards5.0Review for Mastery2-3 Solving Multi-Step Equations Multiply both sides by 2. Then 1 is subtracted. Add 1 to both sides. Then the result isdivided by 2. Divide both sides by 3.Equivalent Equations3x 5 4x 1915y 6 11y 2Add 1 to both sides.15y 11y 6 2Combine like terms.Solve 2x 7 3x 13. Check your answer.2x 3x 7 135x 7 13 7 75x 20205x 55x 42? 77 Divide both sides by 3.Combine like terms.Commutative Property of Addition4y 6 23x 1 723(5) 1 ? 7215 1 ? 7 2ReasonsCommutative Property of Addition7x 5 1914 ? 7 33x 53x 4x 5 19Check: 15153x 12/29/06 5:41:53 PMcontinuedSometimes you must combine like terms before you can use inverse operations to solvean equation.Solve Using Inverse Operations x is multiplied by 3.3x 1 143xClass5.0Review for Mastery2-3 Solving Multi-Step Equations 1 7. Check your answer.Solve 3x23x2( 1) 2(7)Multiply both sides by 2.2 1 1Date4.0,LESSONSolving a multi-step equation is similar to solving a two-step equation. You use inverseoperations to write an equivalent equation at each step.OperationsHolt Algebra 112/29/06 5:41:5315-28 RevMastWB CA.inddPM18LESSON3x 1 7218Copyright by Holt, Rinehart and Winston.All rights reserved.Group like terms together.Combine like terms.Add 7 to both sides.Check:2x 7 3x 13? 132(4) 7 3(4) ? 138 7 12 Divide both sides by 5.? 1313 Solve each equation. Check your answers.5. 5y 4 2y 16Solve each equation. Check your answers.5y 31. 746. 13m 4 10m 23 2m2. 93452127. 3w 7 w 58. 6 7x 5x 2 3 34. 2r5 4 43. 6x5 234Copyright by Holt, Rinehart and Winston.All rights reserved.919Copyright by Holt, Rinehart and Winston.All rights reserved.15-28 RevMastWB CA.indd 19Holt Algebra 1Copyright by Holt, Rinehart and Winston.All rights reserved.512/29/06 5:41:5415-28 RevMastWB CA.inddPM2020Holt Algebra 1Holt Algebra 112/29/06 5:41:54 PM
NameCalifornia StandardsDate4.0,ClassNameCalifornia Standards5.0Review for Mastery2-4 Solving Equations with Variables on Both SidesLESSONVariables must be collected on the same side of the equation before theequation can be solved. 2x 2xSolve 3x 9 4x 9 7x.10x 2x 16? 2( 2) 1610( 2) Add 2x to both sides.8x 16 3xTry x 4.Combine like terms. 3x 3x 9 4x 9 7xAdd 3x to each side.9 9 ? 20 20 Divide both sides by 8.88x 2Check any value of x: 3x 9 3x 9? 4 16 20 168x continuedSome equations have infinitely many solutions. These equations are true for all values of thevariable. Some equations have no solutions. There is no value of the variable that will makethe equation true.Check:10x 2x 16Class5.0Review for Mastery2-4 Solving Equations with Variables on Both SidesLESSONSolve 10x 2x 16.Date4.0,? 4(4) 9 7(4) 3(4) 9 True statement.? 16 9 28 12 9 The solution is the set of all real numbers.? 3 3 Solve 3x 5(x 2).Check:3x 5x 10 5x3x 5(x 2)Distribute. 5xSolve 2x 6 3x 5x 10.? 5( 5 2)3( 5) Add –5x to both sides. 2x 10? 5( 3) 15 10 2x Divide both sides by 2. 2 2x 5Check any value of x:2x 6 3x 5x 10Try x 1.5x 6 5x 10? 15 15 2x 6 3x 5x 10Combine like terms. 5x 5x? 5(1) 102(1) 6 3(1) Add 5x to each side.6 10? 5 102 6 3 False statement.? 511 There is no solution.Write the first step you would take to solve each equation.Possible answers: add 3x to each side, add 7x to each side1. 3x 2 7x2. 4x 6 10x3. 15x 7 3xSolve each equation.Possible answers: add 4x to each side, add 10x to each side7. x 2 x 4no solutionSolve each equation. Check your answers.4. 4x 2 5(x 10)5. 10 y 3 4y 13 486. 3(t 7) 2 6t 2 2t2110. 5x 1 4x x 7Holt Algebra 1DateClassReview for Mastery2-5 Solving ProportionsNameCalifornia StandardsHolt Algebra 1Date12/29/06 5:41:55 PMpartpercentYou can solve percent problems with this proportion: .100whole25x 40Divide both sides by 25.What percent of 86 is 64.5?percentpercentwholepartpercent Sometimes it is necessary to use the Distributive Property.100whole64.5 x86100The part is x.100x 210064.5 is 75% of 86.You can also solve percent problems with this equation:percent whole part20 2x 4Distribute 2. 4Subtract 4 from both sides.2x 2The percent is x.x 7530% of 70 is 21.20 2(x 2)part86x 6450x 21Multiply 4 by 5 and x 2 by 2.wholepartpercent 100whole30x 70100x 1.6 4Class15.0Review for Mastery2-5 Solving Proportions continuedMultiply x by 25. Write the product on the left.Multiply 10 by 4. Write the product on the right.222LESSON25x 404 2 .Solve5x 24 2x 25 1all real numbersFind 30% of 70.2512. 3x 7 2x 4x 1012/29/06 5:41:5515-28 RevMastWB CA.inddPM22Use cross products to solve proportions.x 4.Solve10254x 1025all real numbers11. 2(f 3) 4f 6 6fCopyright by Holt, Rinehart and Winston.All rights reserved.15.0LESSON161no solutionNameCalifornia Standards259. 5 3g 3g 552Copyright by Holt, Rinehart and Winston.All rights reserved.15-28 RevMastWB CA.indd 218. 2x 8 2x 4Possible answers: add 3x to each side, add 15x to each side(as a decimal)36 is what percent of 50?Divide both sides by 2.8 xRewrite:What percent of 50 is 36?Translate:x 50 36Solve:Use the form “percent of whole is part.”Translate into percent whole part.x 0.72Divide both sides by 50.x 72%Write the decimal as a percent.36 is 72% of 50.Solve each proportion.51.252. 12kx 11.208Complete the labels with the words “part,” “whole,” and “percent.”Then find each value.5. Find 16% of 20.x 2.5k 33a 53. 421percent34. 1y 396. What percent of 45 is 6.75?wholepercent3.2wholepart15%Rewrite each problem in the form “percent of whole is part.”7. 14 is what percent of 40?y 30a 10.75Copyright by Holt, Rinehart and Winston.All rights reserved.23Copyright by Holt, Rinehart and Winston.All rights reserved.15-28 RevMastWB CA.indd 238. Find 65% of 80.Holt Algebra 1Copyright by Holt, Rinehart and Winsto
opposites, so they sum to 0 and cancel. Add 4 6. To subtract integers using counters, remember that subtracting a number is the same as adding the opposite of the number. Subtract 5 1 8. To subtract 8, add 8. 5 Add or subtract by drawing a model of two-color counters. 1. 2 ( 5) 2. 4 ( 1
Holt McDougal Algebra 1 77-2-2Factoring by GCFFactoring by GCF Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1. Holt McDougal Algebra 1 7-2 Factoring by GCF Warm Up 1. 2(w 1) 2. 3x(x2 –4) 2w 2 3x3 –12x 2h Simplify. 13 p Find the GCF of each pair of monomials. 3. 4 2 and 6 4.
Robert Gerver, Ph.D. North Shore High School 450 Glen Cove Avenue Glen Head, NY 11545 gerverr@northshoreschools.org Rob has been teaching at . Algebra 1 Financial Algebra Geometry Algebra 2 Algebra 1 Geometry Financial Algebra Algebra 2 Algebra 1 Geometry Algebra 2 Financial Algebra ! Concurrently with Geometry, Algebra 2, or Precalculus
HOLT COUNTY TREASURE OF NORTHWEST MISSOURI is a 2013 Special Section of the Mound City News Published at 511 State St., Mound City, MO 64470 By Holt County Publishing, Inc. PAGE 2 2013 HOLT COUNTY VISITORS' GUIDE SUMMER 2013 Mound City Area Chamber of Commerce We'd Love To Help You Get To Holt County 5 LARGEST TOWNS OF HOLT COUNTY .
En camino Level 1B Humbach, Nancy A. Holt, Rinehart and Winston 002375Y !Ven Conmigo! Holt 2 Spanish TPR STORYTELLING BOOK Muirhead, Pablo Holt, Rinehart and Winston 002376F !Ven Conmigo! Holt Spanish Level 2 Humbach, Nancy A. Holt, Rinehart and Winston 002359J [tú y yo] B Vargas, David Edelsa 004512G
Gene pool The particular combination of alleles in a population at any one point in time. Adapted from Holt Biology 2008 . Adapted from Holt Biology 2008 Adapted from Holt Biology 2008 Chapter 17 Section 1: Genetic Variation Notes . Adapted from Holt Biology 2008 Adapted from Holt Biology
The first of the name in America was Randall or Randolph Holt who came over in The George in 1620. He married Mary Baily of Hog Island, North Carolina in 1626. He was 13 when he came over. They had two sons, John and Captain Michael Holt. (Descendants of John and Isabel Holt) A James Holt, Lancashire, England was buried in 1632 in Bolton Parish.
Polynomial Functions Investigating Graphs of Polynomial Functions Holt Algebra 2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2. Holt McDougal Algebra 2 Investigating Graphs of Polynomial Functions Warm Up Identify all the real ro
Polynomial Equations Finding Real Roots of Polynomial Equations Holt Algebra 2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2. Holt McDougal Algebra 2 Finding Real Roots of Polynomial Equations Warm Up Factor comp
