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College Prep Essential MathChapter 9: Intro to AlgebraMedia LessonSimplify Algebraic Expression – Substitute a Value (Duration 4:51)View the video lesson, take notes and complete the problems below.Variable – A that represents a .Once we the value we can the variable!Evaluate 3𝑥 4𝑦 2 when 𝑥 2 and 𝑦 5.𝑐2Evaluate 3𝑎 4𝑏 when 𝑎 2, 𝑏 3, and 𝑐 6.Media LessonVariables, Expressions, and Equations (Stop at 6:30)View the video lesson, take notes and complete the problems below.Evaluate the expressions given 𝑥 4.𝑥 52𝑥 93𝑥 2 1712

College Prep Essential MathChapter 9: Intro to AlgebraEvaluate the expressions given 𝑥 3 and 𝑦 1.𝑥 𝑦2𝑥 𝑦3𝑥 𝑦 22𝑥𝑦YOU TRY:Evaluate the expressions given 𝑥 4 and 𝑦 1.a) 2𝑥 𝑦b) 𝑦 2 14c) 𝑥 7 𝑦Evaluate the expressions given 𝑎 5, 𝑏 1, and 𝑐 2.e) 2𝑎 5𝑏 7𝑐d) 𝑏 2 4𝑎𝑐13

College Prep Essential MathChapter 9: Intro to AlgebraC. Like Terms and Combining Like TermsAn algebraic expression is made up of terms. Terms are constants or the products ofnumbers and variables. They are separated by addition and subtraction in theexpressions. Examples of terms are 7, 𝑦, 5𝑥 2 , 9𝑎, and 13𝑥𝑦.3𝑥 5𝑦7 𝑡𝑒𝑟𝑚𝑡𝑒𝑟𝑚𝑡𝑒𝑟𝑚In the expression above 3𝑥, 5𝑦, and 7 are terms.Two terms are like terms if the base variable(s) and exponent on each variable areidentical. Below are some examples of like terms.3𝑦 𝑎𝑛𝑑 7𝑦7𝑥 2 𝑎𝑛𝑑 𝑥 28𝑥𝑦 𝑎𝑛𝑑1𝑥𝑦2Like terms can be combined in an expression. To combine like terms we add or subtracttheir coefficients and keep the same variable. When you are asked to simplify anexpression you are asked to combine like terms.Example: Simplify 3𝑥 2𝑥 11.The common terms are 3𝑥 and 2𝑥. These terms are separated by addition, so tocombine them we add their coefficients.3𝑥 2𝑥 11 𝑊𝑒 𝑎𝑑𝑑 3 𝑎𝑛𝑑 2.5𝑥 11Media LessonIdentify Like Terms and Combine Like (Duration 4:36)View the video lesson, take notes and complete the problems below.Which of these terms are like terms? 2𝑥 3 , 2𝑥, 2𝑦, 7𝑥 3 , 4𝑦, 6𝑥 2 , 𝑦 2Simplify each polynomial, if possible.4𝑥 3 7𝑥 32𝑦 2 4𝑦 𝑦 2 2 9𝑦 5 2𝑦14

College Prep Essential MathChapter 9: Intro to AlgebraMedia LessonLike Terms (L2.3) (Duration 6:30)View the video lesson, take notes and complete the problems below.Example 1: Identify the like terms in each of the following expressions.3𝑎 6𝑎 10𝑎 𝑎5𝑥 10𝑦 6𝑧 3𝑥7𝑛 3𝑛2 2𝑛3 8𝑛2 𝑛 𝑛3Example 2: Combine the like terms.3𝑎 6𝑎 10𝑎 𝑎5𝑥 10𝑦 6𝑧 3𝑥7𝑛 3𝑛2 2𝑛3 8𝑛2 𝑛 𝑛3YOU TRY:Simplify the following expression.f) 4𝑥 𝑥 7𝑦 5𝑦 10g) 11 𝑎 6𝑎15

College Prep Essential MathChapter 9: Intro to AlgebraD. Using the Commutative PropertyA helpful tool to simplify expressions is to use the commutative property of addition. Recallthat the commutative property of addition states that the order we add two numbers is notimportant. So, 3 2 is the same as 2 3.When an expression contains more terms, we can rearrange the terms using thecommutative property of addition. We could rearrange the following expression beforecombining like terms.3𝑥 4𝑦 2𝑥 6𝑦3𝑥 2𝑥 4𝑦 6𝑦YOU TRY:Simplify the expression by rearranging the terms.h) 3𝑥 7 4𝑥 5You can decide if you would like to rearrange your terms using the commutativeproperty.16

College Prep Essential MathChapter 9: Intro to AlgebraD. Writing ExpressionsIn many situations we need to know how to translate word phrases into algebraicexpressions. Below is a table of common English words converted into a mathematicalexpression. You can use this table to assist in translating tionWordsExampleAdded to4 added to 𝑛𝑛 4More than2 more than 𝑦𝑦 2The sum ofThe sum of 𝑟 and 𝑠𝑟 𝑠Increased by𝑚 increased by 6𝑚 6The total ofThe total of 8 and 𝑥8 𝑥Plus𝑐 plus 2𝑐 2Minus𝑥 minus 1𝑥 1Less than5 less than 𝑦𝑦 5Less4 less 𝑟4 𝑟Subtracted from3 subtracted from 𝑡𝑡 3Decreased by𝑚 decreased by 10𝑚 10The differenceThe differencebetweenbetween 𝑥 and 𝑦Times12 times 𝑥OfOne-third of 𝑣The product ofThe product of 𝑛 and 𝑘Multiplied by𝑦 multiplied by 3TwiceTwice 𝑑Divided by𝑛 divided by 4The quotient ofThe quotient of 𝑡 and 𝑥DivisionTranslation𝑥 𝑦12 𝑥1𝑣3𝑛𝑘 𝑜𝑟 𝑛 𝑘3𝑦2𝑑 𝑜𝑟 2 𝑑𝑛4𝑡𝑥17

College Prep Essential MathChapter 9: Intro to AlgebraLet us first review.Media LessonTranslating Word Statement to Math (Duration 3:54)View the video lesson, take notes and complete the problems below.The sum of 3 and 8.The sum of 7 and 12.The difference of 𝑥 and 𝑦.The difference of 7 and 12.The difference of 𝑛 and 4.The sum of five and three is eight.The difference of two and seven is negative five.The sum of five, three, and six is fourteen.The difference of nine, three, and four is two.Media LessonEx: Write an Algebraic Expression in the Form x c and c-x(Duration 1:12)View the video lesson, take notes and complete the problems below.Write this English phrase as an algebraic expression. Let the variable 𝑥 represent thenumber.𝑠𝑒𝑣𝑒𝑛 𝑚𝑜𝑟𝑒 𝑡ℎ𝑎𝑛 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟Write this English phrase as an algebraic expression. Let the variable 𝑥 represent thenumber.4 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟18

College Prep Essential MathChapter 9: Intro to AlgebraYOU TRY:Write the phrase as an algebraic example.i) The difference of 17 and a numberj) The sum of a number, 3, and 619

College Prep Essential MathChapter 9: Intro to AlgebraEXERCISESIn the following exercises, evaluate the expression for the given value.1) 7𝑥 8 when 𝑥 22) 9𝑥 7 when 𝑥 33) 8𝑥 6 when 𝑥 74) 𝑥 2 when 𝑥 125) 𝑥 2 3𝑥 7 when 𝑥 46) 2𝑥 4𝑦 5 when 𝑥 6 and 𝑦 97)𝑎𝑏 1when 𝑎 10 and 𝑏 48)3𝑎2𝑏 1when 𝑎 11 and 𝑏 1In the following exercises, identify all sets of like terms.9) 3𝑥, 5, 𝑥 2 , 11, 18𝑥10) 2𝑦, 𝑦 2 , 𝑥, 11, 5𝑦11) 2𝑥, 15𝑦, 9𝑥, 𝑦, 2𝑦12) 8𝑎, 5𝑎2 , 3, 17𝑎, 𝑎220

College Prep Essential MathChapter 9: Intro to AlgebraIn the following exercises, simplify the given expression by combining like terms.13) 10𝑥 3𝑥14) 15𝑥 4𝑥15) 2𝑥 7 6𝑥16) 4𝑐 𝑐 2𝑐17) 9𝑥 3𝑥 818) 8𝑎 5𝑎 919) 8𝑑 6 2𝑑 520) 7𝑝 6 5𝑝 421) 10𝑎 7 5𝑎 2 7𝑎 422) 4𝑥 3 8𝑥 921

College Prep Essential MathChapter 9: Intro to AlgebraCheck your work with the answer key!Online QuizLog on to Canvas to take the section quizDirections: It is very useful to save your math exercise work and use it as a chaptertest review when you study for your chapter test and final.7) Write each question on the screen down to for your record8) Solve the problem step by step below each question9) Double check your work to see whether your answer make sense10) Enter your answer in the answer box in Canvas. Make sure you click on the“Preview” button to make sure you enter the right format before you submit youranswer. If you are not sure how to enter your answer with the correct format, askyour instructor.11) If you did not answer the question correctly, solve the question again from thebeginning below your 1st attempt. Sometimes, it is better to start a problem againfrom the beginning and compare your steps with your 1st attempt to figure out yourmistake.12) Insert your work at the end of each section in your workbook so that you can use itto study for your chapter test later.22

College Prep Essential MathChapter 9: Intro to AlgebraSection 9.3 Solving EquationsA. Solving One Step EquationsAn equation is a mathematical statement that uses an equal sign. The following areequations:𝑥 1 103𝑦 10 2𝑥 114When we solve an equation, we are looking for the value of our variable that would makethat statement true. We call this value the solution of the equation.Can you recognize the solution to 𝑥 1 10? The solution is 9. We say 9 is a solutionto 𝑥 1 10 because when we substitute 9 for 𝑥 the resulting statement is true.𝑥 1 109 1 1010 10 Sometimes the answer is not as obvious. We solve an equation by a process calledisolating the variable. When we isolate a variable, we “unattach” any constants andcoefficients that are on the same side of the equal sign as our variable. We make use ofopposite operations— addition and subtraction are opposites and multiplication anddivision are opposites.Addition and SubtractionExample: Solve 𝑦 10 2.We begin by unattaching the constant 10. In the equation our constant is beingsubtracted, to unattach it we do the opposite operation, addition. We add 10 to both sidesof our equation.𝑦 10 2 10 10𝑦 12Our solution is 𝑦 12. You can check this is correct because 12 10 2.23

College Prep Essential MathChapter 9: Intro to AlgebraMedia LessonEx: Solve One Step Equations by Add and Subtract Whole Numbers(Duration 5:00)View the video lesson, take notes and complete the problems below.Examples: Solve.𝑥 9 24𝑥 7 32Media LessonEx: Solving One Step Equation by Add/Subtracting Integers(Duration 3:17)View the video lesson, take notes and complete the problems below.Examples: Solve.𝑥 7 24𝑥 9 21YOU TRY:Solve. Substitute your answer back into the equation to check your solution.k) 𝑥 4 15l) 𝑦 7 1524

College Prep Essential MathChapter 9: Intro to AlgebraMultiplication and DivisionExample: Solve 3𝑦 12.We want to isolate the variable 𝑦. We begin by unattaching the coefficient thataccompanies it. In the equation 𝑦 is being multiplied by the coefficient 3. The opposite ofmultiplication is division. We divide by 3 on both sides of the equation.3𝑦 12 33𝑦 4Our solution is 𝑦 4. You can check this is correct because 3 4 12.Media LessonEx: Solve One Step Equation By Mult And Div Whole Numbers(Duration 2:53)View the video lesson, take notes and complete the problems below.Examples: Solve.𝑥 3635𝑥 35Media LessonEx: Solving One Step Equation by Mult/Div Intergers (Duration 2:45)View the video lesson, take notes and complete the problems below.Examples: Solve. 6𝑥 36 𝑥 8325

College Prep Essential MathChapter 9: Intro to AlgebraOften we might get close to solving for 𝑥 only to get a solution like this 𝑥 3, where anegative sign is in front of our variable. To get our final answer we can multiply bothsides by -1. This gives us 𝑥 3 1( 𝑥) 1(3)𝑥 3A shortcut is to just change all signs to their opposites. For example, for 𝑥 4 the 𝑥and 4 are negative. We change them both to positive and get 𝑥 4.YOU TRY:Solve. Substitute your answer back into the equation to check your solution.m) 5𝑥 25n) 3𝑎 36o) 𝑥 5FractionsSolving an equation with fractions will have the same steps as solving our previousequations. The only difference is when we have a fraction as the coefficient of ourvariable, we can use the reciprocal to unattach the coefficient.1Example: Solve 2 𝑥 1312The coefficient of 𝑥 is 2. We will multiply by the reciprocal 1 on both sides of theequation.1𝑥 1322 12( 𝑥) (13)1 21𝑥 (13)2𝑥 26𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑏𝑦 𝑡ℎ𝑒 𝑟𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙26

College Prep Essential MathChapter 9: Intro to AlgebraMedia LessonSolve One Step Equations with Fractions (Duration 8:33)View the video lesson, take notes and complete the problems below.𝑥 11 20 5𝑥 315𝑥 4282 3 3 46𝑥 415414 𝑥 915YOU TRY:Solve.3k) 4 𝑎 811l) 𝑛 4 8 227

College Prep Essential MathChapter 9: Intro to AlgebraCombining Like TermsIt makes it easier to solve an equation if we combine like terms. If there are like termson the same side of the equal sign, we begin by combining them before isolating thevariable.Media LessonOne Step Equations – Simply First (Duration 4:39)View the video lesson, take notes and complete the problems below.Always each side before .5𝑥 3 4𝑥 715 7 8𝑥 6𝑥YOU TRY:Solve. Substitute your answer back into the equation to check your solution.p) 𝑥 8 12 5q) 7𝑥 3𝑥 70 4628

College Prep Essential MathChapter 9: Intro to AlgebraB. Solving Two-Step EquationsWhen solving equations it helps to think about how each thing is attached and how orderof operations would be applied. We need to “undo” the order of operations, so we workbackwards.We first undo addition and subtraction. Then we undo multiplication and division.Media LessonTwo Step Equations – Basic Two Step (Duration 4:39)View the video lesson, take notes and complete the problems below.Simplifying we use order of operations and we before we.Solving we work in reverse so we will first and thensecond.5𝑥 7 8 9 5 2𝑥Media LessonTwo Step Equations – Fractions (Duration 4:53)View the video lesson, take notes and complete the problems below.A fraction bar is the same as .To clear division we will both sides by the.Because we are solving and working backwards to our solution we willand then .𝑥 3 74 2 4 𝑥629

College Prep Essential MathChapter 9: Intro to AlgebraYOU TRY:Solve. Substitute your answer back into the equation to check your solution.r) 5𝑥 7 37s) 7 2𝑥 9t)𝑥4 1 7𝑥u) 10 3 2130

College Prep Essential MathChapter 9: Intro to AlgebraC. Solving Multi-Step EquationsIf there is a variable on both sides of the equal sign, we must first get our variables on thesame side of the equation. We move the variable with the smaller coefficient. To move itwe add its additive inverse to both sides.Example: Solve 2𝑥 7 3𝑥 22There is an 𝑥 on both sides of the equal sign. The first step is to move 3𝑥 since it hasthe smaller coefficient. The additive inverse of 3𝑥 is 3𝑥.6𝑥 4 3𝑥 22 3𝑥 3𝑥𝑀𝑜𝑣𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 𝑡𝑜 𝑠𝑎𝑚𝑒 𝑠𝑖𝑑𝑒.9𝑥 4 22 4 4𝑈𝑛𝑑𝑜 𝑎𝑑𝑑𝑖𝑡𝑜𝑛.9𝑥 18 99𝑈𝑛𝑑𝑜 ��𝑛.𝑥 2The guidelines to solve algebraic equations are:1)2)3)4)Collect like terms that are on the same side of the equal sign.Move variables to the same side of the equal sign.Undo addition and subtraction.Undo multiplication and division.Media LessonSolve an Equation with Variables on Both Sides (Duration 3:55)View the video lesson, take notes and complete the problems below.Solve 7𝑥 2 3𝑥 1831

College Prep Essential MathChapter 9: Intro to AlgebraYOU TRY:Solve.v) 2𝑥 7 3𝑥 22w) 6𝑛 2 3𝑛 7D. Writing EquationsWe can combine our knowledge of solving an equation and writing variable expression tosolve word problems. An equation has an equal sign. So if we have a sentence that tellsus that two phrases are equal, we can translate it into an equation. We look for clue wordsthat mean equals.EqualsIsAreEqualGivesIs equal toIs equivalent toYieldsResults inwasExample: Write an equation for the following and then solve.Twice a number is 16, find the number.We first will translate it to an equation by finding key terms.𝑇𝑤𝑖𝑐𝑒 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑠 16, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟.2 𝑡𝑖𝑚𝑒𝑠𝑥 The location of “is” tells us the equal sign is between 𝑥 and 16.2𝑥 16We have our equation. We can now solve.2𝑥 16 22𝑥 8This answer makes sense because twice of 8 is 16.32

College Prep Essential MathChapter 9: Intro to AlgebraYOU TRY:Translate the sentence into an algebraic equation.x) Three more than 𝑥 is equal to 47.33

College Prep Essential MathChapter 9: Intro to AlgebraExercisesSolve the following equations.1) 𝑥 7 172) 𝑥 8 223) 𝑥 13 104) 𝑥 4 155) 𝑥 21 156) 𝑥 15 42247) 𝑥 5 518) 𝑥 3 2Solve the following equations.9) 2𝑥 1210) 3𝑥 2411) 4𝑥 1612) 7𝑥 4213) 72 12𝑦14) 8𝑥 5615)𝑥4 15𝑥16) 2 1434

College Prep Essential Math𝑥17) 3 12319) 5 𝑥 15Chapter 9: Intro to Algebra18)𝑥9 6520) 8 𝑥 40Solve the following equations by combining like terms.21) 5𝑥 3𝑥 1022) 4𝑥 7𝑥 3323) 5𝑥 72 4724) 9𝑥 42 335

College Prep Essential MathChapter 9: Intro to AlgebraSolve the following two step equations. Check your answers.25) 22 5𝑥 726) 7𝑥 2 5127) 50 8𝑥 1028) 41 9𝑥 529) 4 3𝑥 2230) 3 8𝑥 5331) 5𝑥 3𝑥 2 1832) 7𝑥 2𝑥 7 11Solve the following equations. Check your answers.33) 6𝑥 15 5𝑥 334) 4𝑥 17 3𝑥 235) 4𝑥 5 𝑥 4036) 9𝑥 7 2𝑥 3737) 5𝑥 6 2𝑥 1538) 4𝑥 3 8𝑥 939) 7𝑥 3𝑥 2 5 2𝑥 940) 2𝑥 7 12 3𝑥 5𝑥 7𝑥 1036

College Prep Essential MathChapter 9: Intro to AlgebraIn the following exercises, translate to an equation and then solve.41) Five more than 𝑥 is equal to 21.42) The sum of 𝑥 and -5 is 33.43) Three less than 𝑦 is 19.44) The sum of 𝑦 and 3 is 40.45) The difference of 9𝑥 and 8𝑥 is 17.46) The difference of 5𝑐 and 4𝑐 is 60.37

College Prep Essential MathChapter 9: Intro to AlgebraCheck your work with the answer key!Online QuizLog on to Canvas to take the section quizDirections: It is very useful to save your math exercise work and use it as a chaptertest review when you study for your chapter test and final.1) Wr

College Prep Essential Math Chapter 9: Intro to Algebra 2 SECTION 9.1 Properties of Algebra A. Identity Properties of Addition and Multiplication There are two properties of algebra that you are probably very familiar with. What happens when you add zero to a number? The sum of any number and zero is the number itself.