Integrated Algebra A

NameDateIntegrated Algebra ANotes/HW Packet 2LessonHomeworkTranslating Words into Algebraic ExpressionsHW1Translating Words into Algebraic EquationsHW2Variables & Like TermsHW3One-Step Equations (Add/Subt/Mult/Div)HW4Solving Two-Step EquationsHW5Solving Multi-Step Equations with the Distributive PropertyHW6Solving Equations with Variable on Both Sides of Equal SignSolving Equations with Dist. Property & Variable on BothSidesHW7Equation ReviewReview SheetTestHW8Completeworksheet

Translating Words into Algebraic ExpressionsWe don’t only use the terms, add/subtract/multiply/divide when talkingabout operations. Fill in the chart with other terms that can be used forthese operations. -xWays to write the operationx Emphasis on “less than”Example: If I were to say, “How much is three less than five?” you are doing themath in your head. What you are doing in your head, even though it is an easyquestion, is “5 - 3.”So when you see the words “less than” or a version of it, you must theterms and put a sign in between them. (This also applies toterms with the word ‘from.’Examples:1) Five less than x.2) Eight subtracted from g.3) y less than fifteen.

Parentheses: Some phrases are worded in a way that you need parentheses tomake the problem make sense. Commas are sometimes used to specifyparentheses, and phrases such as “4 times the sum of ”Examples:1) The product of x and y, decreased by 22) The sum of 10 and a number, divided by 33) Nine times the sum of x and 64) 11 times the difference of 3 and yPracticeUse mathematical symbols to translate the following verbal phrases into algebraiclanguage:1) w more than 32) r decreased by 23) The product of 5r and s4) The sum of t and u, divided by 65) Twice the sum of x and y6) Five times the sum of a number and 8Using the letter n to represent “a number”, write each verbal phrase as an algebraicexpression:1) A number increased by 122) 7 less than a number3) 4 added to twice a number4) The sum of a number and 5, decreased by 75) 4 more than two thirds of a numberWord Problems:Ex. 1: Represent the following by an algebraic expression:“a distance that is 20 meters shorter than x meters”

Translating Words into Algebraic EquationsExpressions cannot be solved because they do not have an equal sign. Equationson the other hand have an equal sign! Yesterday, we learned how to translatewords into algebraic expressions and today we are going to take that one stepfurther!Words that indicate when to put an “ “ sign: is equals the result is exceeds byTranslate the following sentences into equations.1. Four times a number is 20.*Can you figure out what “the number” is?2. A number decreased by 6 equals 8.*Can you figure out what “the number” is?3. A number divided by 2 is 4.*Can you figure out what “the number” is?4. 5 times a number, decreased by 7 is 13.5. When a number is subtractedfrom 8, the result is 10.6. 9 less than twice a number is 10.7. The sum of 50 and a number is equal to6 times that number.8. 4 times a number increase by 5 exceedsthe number by 10.

Classwork:A. Translate these expressions.1. Twice a number, increased by 82. 4 times the sum of a number and 73. 3 less than 6 times a number4. The sum of a number and 5, divided by 3B. Translate these equations.1. If two-thirds of a number is diminishedby 8, the result is 32.2. 10 times a number increased by 6 is 112.3. When a number is doubled, the result is 24.4. The product of a number and 11 is 99.5.7 times the sum of a number and 4exceeds 3 times that number by 17.

NameDateHW #2Match the following words to the correct expressions:1. 3 less than twice a numberA. n - 62. 8 more than 4 times a numberB.3. 6 less than a numberC. 3( y - 2)4. 3 times the difference of a number and 2D. 2d – 35. a number decreased by 3E. k – 36. 8 multiplied by the sum of a number and 4F. 8 4x7. a number diminished by 6G. h – 68. one-third of a numberH. 8(f 4)x3Translate the following words into algebraic equations.1. A number increased by 3 is 14.2. 4 times a number decreased by 6is equal to 6 times that number.3. The sum of 50 and a twice a numberequals 30 minus that number.4. A number plus 15 exceeds twice thatnumber by 3.5. Three-fourths of a number less than 6 is 10.6. Three times a number decreased by 8 isequal to 4 times that number increased by 12.Review:Which transformations preserve congruence (keeps the figures the same shape andsame size)?

Variables and Like TermsVocabulary1) Variable -2) Coefficient -3) Term -4) Like terms -5) Simplify -Number of terms: We count how many terms a polynomial has after combining alllike terms.One termTwo termsThree termsFour termsEx:Ex:Ex:Ex:We cannot count the number of terms unless all of the like terms have been puttogether so we must combine the like terms. When combining like terms you haveto pay attention to the attached and the infront of the coefficient.Combining Like TermsSteps: Identify like terms. Combine the coefficients of the like terms and keep the common variableattached. Repeat this process for all sets of like terms. Separate all of your answers with addition/subtraction signs.Examples:1) 5x 3x2) 5m2 – 1m2 8m – 3m2 6m3) 1xy 3n – 2n 4xy – 54) 4a – 12b 165) 10x2 x – 7x2 – x

Practice1. 5x 7x2. -3x2 10x23. 13c – 12c4. 19y y5. 3yz – 5yz6. –e 8e7. 4a 9 a8. 7s 5x – 8s9. 4.7x – 5.9x10. 5x – 6y – 8y 7x11. 23x 8 6x 3y12. 4a2 – 3 – 2a213. 10b2 – 9b – 4b2 6b14. 5y2 y – 7y2 - y

NameDateHW #3Practice1. 20n 30n2. 15x2 (-3x2)3. 6x – 11x4. m m 4m5. 2abc – 6abc6. –f – 10f7. 5z 3 – z8. 9p 15r 8p9. –9k 14k10. 7s 6u – 5s – 10u11. 8h – 4g – 8h 4g12. –9x2 1 – 3x213. 40y2 16y – 15y – 13y214. 8u3 5u – u2 6u – 3u3 u2

Solving One-Step Equations ( /-)Now that we know how to set up equations, we are going to solve them usingaddition and/or subtraction!Example 1:x 4 7[Subtract 4 from each side to undo the addition] [Here is your answer!]Example 2:y – 3 12[Add 3 to each side to undo the subtraction] [Here is your answer!]Our Goal:To isolate the variable (get the variable by itself on one side).Solve the equation [Show ALL Work!]:1) x 4 – 72) x 5 103) t – 2 64) 11 r – 45) -9 2 y6) n – 5 -97) -3 x 78)21 a 559) r – (-7) 16

One-Step Equations ( / )Today we are going to solve equations dealing with multiplications and division.Example 1:6x 18[Divide each side by 6 to undo the multiplication] [Here is your answer!]Example 2:y 9 3[Multiply both sides by -3 to undo the division] [Here is your answer!]Example 3:2x 45[Multiply both sides by the reciprocal to get rid of the fraction] [Here is your answer!]Solve the equation [Show ALL Work!]:1) 7x 144)1y 1047) 12x - 482) -6x 243)y -485) - 81 -9n6)x -1 38) 3n 1249) -20x -20

NameDateHW #4SHOW ALL WORK on here or another sheet of paper!

Solving 2-Step Equations Solving equations is just a matter of undoing the operations that are being doneto the variable. We already did 1-step equations Example 1:Example 2:x – 3 -9Operation Now:-5x 30Operation Now:Opposite Operation:Opposite Operation:AnswerAnswer In an equation which has more than one operation, we have to undo theoperations in the correct order. First, undo addition or subtraction, then undomultiplication or division.Example 1:5x – 2 13Let’s check our answer!Example 2:1x 6 22CheckExample 3:7 – x -15Check

Classwork: Show all steps and check the odd problems!1. 6x – 2 22Check2. 2x 8 63.1m 7 103Check4. 16 – 8r 405. 6 -3x4 -12Check

NameDateHW #5“What do you call a crate of mallard ducks?”Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke.1) 3x 2 262) 4x – 5 353) 2x 3 13I. 1A. 0B. 5K. 64) -7x – 7 495) 10 – 6x 466) 9 6 – xN. 7E. -6O. -4Q. -57) 2x – 1 -98) -7 – 9x -619) -23 7 – 15xZ. 18X. 2L. -9S. 810) 14x 6 611) -1 – 8x 712) 16 -3x 1R. -1F. -8M. 11D. 9C. 10D. 9103797412610285111C. 10W. 14U. -3

Solving Multi-Step Equations with DistributionDo you remember how to use the Distributive Property? Let’s see:1)5(x 2)2)-2(6 – x)Do you remember how to solve 2-step equations? I hope so! Let’s try:1)5x – 2 182)7 – x -10Now, let’s put these two together and solve multi-step equations using thedistributive property!Steps:Check:Distribute the 5.Example 1:5(x – 7) 90Add 35 to both sides.Divide by 5 on bothsides.Example 2:3(x – 2) 18Example 3:1(x 6) 122Check:Check:IMPORTANT:Leave theterm with thevariableALONE untilthe last step!

Example 4:4x – 3(x – 2) 21Steps:Distribute the –3 first!!!Check:(Bring down the 4x)Combine like terms.Subtract 6.Example 5:-2(4 – x) – 5 11Practice:1)3(y – 9) 304)9t – (2t – 4) 252)6(2 – x) 65)3)5x 3(x 4) 28-8(2 – x) – 4(x – 2) 8

NameDateHW #6“Who wrote the book ‘Grocery Packing at theSupermarket’?”Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke.1. 3(x 2) 212. 5(2x – 1) -253. –4(3x – 5) -16M. 7R. 1S. 3Z. 94. –2(4 – x) – 5 115. 3(-6x 7) 4x -76. 2(3x – 4) 5(2x 3) -9E. -5A. -2U. 4W. -11C. -187. 5(x 9) 658.1(x – 3) -429. 5x 2(x – 6) 7 2B. -1T. NoSolutionD. -8F. 25G. 1210. 9(x 3) - 14x – 15 52L. 5O. 6S. 297538110624

Solving Equations with Variable on Both SidesSuppose there are variables on both sides of the equation. The trick now, is toget the variables on the same side by adding or subtracting them.Example 1:4x 5 x – 4We need to get the x overwith the 4x so we willsubtract it from both sides.Now we are at a 2-stepequation! Let’s subtract 5from both sides.Divide by 3!Example 2:3x – 5 5x 7Check:Example 3:7y 5 – 3y 1 2y 2Check:Check:

Example 4:4x – 7 6x 5 - 2xSomething weird is goingto happen here!Practice:1. 12x – 9 4x 15Check:2. 5 3x 28 7x – 7Check:

NameDateHW #7“Who wrote the book ‘Terrible Weather’?”Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke.1. 5x – 7 4x 32. 6 2x 7x - 93. 8x 1 -8 - xB. 4Y. NoSolutionN. 104. –5 12x 18x 75. –4x 3 5x – 13 - x6. –10 – 11x 24 3xI. -11S. -2P. -3V. -7E. 17. 8 3x x 11 2x8. 5 17x 9 23x 149. –7x 18 -7 – 2xW. 5F. -6O. 3A. -1R. 210. –12 – x 2x 6 3xW. 8Y. -13D. 093716852104

Solving Equations w/Variable on Both Sides and DistributionDistribute the following:1)-8(x – 2)2)7(4 – x)4)-14 5 – x – 3 4xCombine like terms:3)-5x 2 7x - 14Solve equations with Variables on BOTH sides (Combine Like Terms First for #6):5)3x 5 4x 2.56)2x 4 – 3x -9 x 5Now, let’s put these three concepts together:Example 1:2(4x 15) 7x 3Steps:1) Distribute the 2.2) Subtract 7x fromeach side.3) Subtract 30 fromeach side.Check:

Example 2: 4(x – 5) 2 x 3Steps:1) Distribute the 4.2) Combine Like Terms.3) Subtract x from eachside.Check:4) Add 18 to each side.5) Divide both sidesby 3.Practice:1) 15x 29 2(3x – 1)2)22x 16 3(5x 4)3) 100(x – 3) 50(9 – x)4)9x – (2x – 4) 16 x

NameDateHW #8Solve:1)4(2 – x) 242)6x 2(4x – 1) 263)-3x 14 -5x4)2x – (5x – 4) 4(-x 1)5)-5(2x – 7) – x 2(x 2) – 86)5x – (6 – x) 2(x – 7)

[Divide each side by 6 to undo the multiplication] [Here is your answer!] Example 2: 3 y 9 [Multiply both sides by -3 to undo the division] [Here is your answer!] Example 3: 5 2 x 4 [Multiply both sides by the reciprocal to get rid of the fraction] [H