Date Lesson Text TOPIC Homework. Verifying Equations WS 3.1. Solving Multi-Step Equations WS 3.3. Solving Equations with Rationals WS 3.

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1 UNIT 3 EQUATIONS Date Lesson Text TOPIC Homework Verifying Equations WS Solving Simple Equations Pg. 193 # 6 8, 12 Use any method you wish. Verify answers to # Solving Multi-Step Equations WS Solving Equations with Rationals WS MORE Solving Equations with Rationals Pg. 208 # 1 4, Introduction to Word Problems WS MORE Word Problems WS EVEN MORE Word Problems Work Period WS Using Formulas Pg. 215 # 1, 2, 6a-d, 8, 15, Unit 3 Review Pg. 230 # 1, 2, 4, 5, 7, 8, 9, UNIT 3 TEST

2 MPM1D Lesson 3.1 Verifying Equations YOU DO IT! Do examples 1 and 2 in your groups. Ex. 1 Solve each of the following equations by inspection. (Determine which value of the variable will make the statement true no need to show your work). a) a a = b) 2b 7 31 b = c) 3 2c 7 c = d) 5d 8 31 d = e) 10 5( e 4) e = Ex. 2 A possible solution is shown for each equation. Is this solution correct? (Yes or No) There is no need to show your work (try them in your head!!). a) 3a 4 11 Solution: a = 6 Yes or NO? b) 3b 4 2b 1 Solution: b = 5 Yes or NO? c) 9cc 3 Solution: c = 3 Yes or NO? d) 3(5d 1) 12 Solution: d = 1 Yes or NO? Ex. 3 Use a formal verification to determine if the given value is the correct solution to the given equation. 3b a) 2(2 3 a) 14 a b) 1 2( b 3) 4 Solution: a = 2 Solution: b = 8 WS 3.1

3 MPM1D Lesson 3.2 Solving Equations To solve an equation means to find the value of the variable that makes the equation true. ie: x 37 x 4 To solve an equation you must eliminate all the constants on the same side of the equation as the variable. to eliminate addition of a number, you subtract that number from both sides of the equation to eliminate subtraction of a number, you add that number from both sides of the equation to eliminate multiplication by a number, you divide by that number on both sides of the equation to eliminate division by a number, you multiply by that number on both sides of the equation To keep an equation balanced, whatever operation you do to one side of the equation, You must do to the other side of the equation. ie: x + 3 = 7 x = 7 3 x = 4 When you eliminate constants you must do it in order of SAMDEB! Ex. 1 Solve each of the following equations algebraically. Show your work. a) 2a 7 23 b) 2b 3 7

4 d c) 4c 8 12 d) f e) e 7 2 f) 35 2 A QUICKER WAY----- TRANSPOSING! Let s look at 2a 7 23 again.

5 Let s try a few examples using the method of transposing. It will help us save a lot of work when equations become more complicated. Ex. 2 Solve each of the following equations algebraically. Verify each of your answers. a) 3a 6 12 b) 2b 9 8 c c) Pg. 193 # 6 8, 12 Use any method you wish. Verify answers to # 12

6 MPM1D Lesson 3.3 Solving Multi-Step Equations When you have more than one variable term, you must gather like terms. Gather the variables on one side of the equation and constants on the other using the transposing method. *** Solutions to an equation are also called roots.*** Ex. Solve each of the following algebraically, verify a), d), and f). a) 3a17 2a 28 b) 4 5b 8 b c) 6c 7 2c 21

7 d) 4 2d 16 d 5 e) 2( e 3) 14 ( e 7) f) 9 (2 f 4) 3(2 f 7) WS 3.3

8 MPM1D Lesson 3.4 Solving Equations with Rationals To solve equations with rationals. 1 Eliminate all denominators by multiplying each term by the common denominator. ******* you may wish to gather constants before eliminating the denominator 2 Solve for the variable. 3 Check your answer before moving on! Ex. Simplify each of the following. 3a a) 15 5 b) 5b b c) 8c 3c Ex. Solve each of the following. Verify d) and f) a 1 a) 1 4 b) 6 ( 2) 3 3 b c c c)

9 1 4 3 (2d 7) e) 1 e e d) d f) 3 f 5 5 e WS 3.4

10 MPM1D Lesson 3.5 MORE Solving Equations with Rationals Ex. Solve each of the following. Verify d) a) 3 x 1 2 x 7 b) 2 x 1 8 x c) 1 ( x 4) 3 (2x 7) d) 1 (2x 3) 4 2 ( x 5) Pg. 208 # 1 4, 11

11 MPM1D Lesson 3.6 Introduction to Solving Word Problems with Equations The hardest thing about solving word problems is taking the problem written in English and translating into math. Usually, once you get the math equation, you will be fine, but actually getting that equation can sometimes seem almost impossible. The following is a list of hints and helps. To really learn how to solve word problems, you will have to practice, practice, practice. ALGORITHM 1 Read the entire problem carefully. Determine what information you are given and what you are asked to find. 2 Work in an organized manner. Introduce variables to represent the unknown(s) in an opening statement. If appropriate for the question draw and label diagrams neatly. Determine what the problem is actually asking for. 3 Look out for KEY WORDS below is a partial list. ADDITION SUBTRACTION MULTIPLICATION DIVISION EQUALS increased by more than combined, together total of sum or added to decreased by minus or less difference between/of fewer than less than is backwards in English compared to what it is in math product of of times increased/decreased by a factor of per out of ratio of quotient percent (out of 100) is, as, was, will be gives result is

12 4 Based on the information in the question, construct an equation that represents the situation in the problem. 5 Solve the equation. 6 Solve the problem and state your answer in a closing statement. Ex. 1 Write an algebraic expression for each of the following. Let n represent the number. a) a number increased by ten b) four less than twice a number c) the product of five and a number d) the sum of three consecutive integers Ex. 2 Translate each of the following into an equation. Let n represent the number. a) the sum of three and twice a number is thirteen. b) If four is subtracted from six times a number, the result is twelve. Ex. 3 Justin and Zeena both participated in a charity walk-a-thon. Justin raised $10 more than twice as much as Zeena. If they raised a total of $610, how much did each raise?

13 Ex. 4 One number is four less than twice another number. Twice the larger number is equal to three times the smaller number. Find the numbers. Ex. 5 Amani, Barack and Claire have part-time jobs. Last week, Claire earned twice as much as Amani, while Barack earned $25 more than Claire. If they earned a total of $450 how much did each earn? WS 3.6

14 MPM 1D Lesson 3.7 MORE Word Problems Ex. 1 A number doubled and increased by four is equal to the sum of two and four times the same number. Find the number. Ex. 2 One number is 11 less than another number. The larger number in creased by one is equal to four times the smaller number. What are the numbers?

15 Ex. 3 Samantha scored 4 more than twice the number of goals that Greta did. In total, they scored 37 goals. How many goals did each score? WS 3.7

16 MPM 1D Lesson 3.9 Working with Formulas Ex. 1 The width of a rectangular garden must be 15 m. Determine what the length of the garden will be if the perimeter is 70 m. N.B. P = METHOD 1: USE THE FORMULA FOR PERIMETER METHOD 2: MAKE A FORMULA FOR LENGTH

17 Ex. 2 Rearrange each formula to isolate for the indicated variable. a) y mx b, for b b) a bc 3, t for c c) 2, A r for r Pg. 215 # 1, 2, 6a-d, 8, 15, 16

ALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations

ALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations ALGEBRA 1 Interactive Notebook Chapter 2: Linear Equations 1 TO WRITE AN EQUATION: 1. Identify the unknown (the variable which you are looking to find) 2. Write the sentence as an equation 3. Look for