Solving Equations.notebook October 01, 2014

Transcription

1 Algebraic Expressions 1

2 Warm-up: Fill-in the blank. The product is the answer to a problem. The difference is the answer to a problem. The quotient is the answer to a problem. The sum is the answer to a problem. 2

3 What words or phrases can be used to represent the operations? Addition Subtraction Multiplication Division 3

4 Evaluating Algebraic Expressions variable - a letter or symbol that represents an unknown value Ex: substitution - replacing a variable with a value Ex: term - part of an algebraic expression that can be a number, a variable, or a product of both Ex: In the expression 2x + 14 the terms are 2x and 14 coefficient - the numerical factor in the term of an algebraic expression Ex: 4

5 Simplifying Algebraic Expressions like terms - terms that have the same variables with the same corresponding exponents Ex: In the expression 2x x + 1, the terms 2x and x are like terms, as are 4 and 1 equivalent expressions - expressions that are equal for all values of the variable Ex: simplify - to write an equivalent expression by combining like terms Ex: 5

6 Mathematical Properties commutative property - a + b = b + a associative property - (a + b) = c = a + (b + c) distributive property - a (b + c) = (a b) + (a c) 6

7 Solving Equations When solving equations, the objective is to get the variable on one side of the equation and everything else on the other. In order to do this, you must "undo" the equation. Undoing an equation means that you perform opposite operations. Addition and Subtraction are opposite operations. Multiplication and Division are also opposites. 7

8 ex. 1: x + 1 = 5 ex. 2: x 4 = 15 ex. 3: 12 x = 8 ex. 4: 20 = 14 x 8

9 ex. 5: 4x = 12 ex. 6: = 12 9

10 ex. 7: ex. 8: 10

11 Multi Step Equations Write these problems down! ex. 9: ex. 10: 11

12 ex. 11: 0.8z = z

13 ex. 12: 4y 1 = 2(y 2) 13

14 A.REI.3: Solve linear equations in one variable, including equations with coefficients represented by letters Solving Equations in One Variable Some equations may have no solution. For example, when solving results in something impossible, like 2 = 6. Solve the equation 2(3x + 1) = 6x Some equations will have infinitely many solutions. For example, when solving results in the same value on each side of the equal sign, such as 2x = 2x. Solve the equation 3(4x + 2) = 12x + 6. Other equations will only have one solution. For example, when solving results in the variable equal to a number, such as x = 5. Solve the equation 5x + 9 = 2x

15 ex. 13: Does this equation have one solution, no solutions, or infinitely many solutions? 10q 15 = 5(2q + 4) 15

16 Worktime: Solving Equations y = 4y 2. r 4 + 6r = 3 + 8r 3. 6(2x 4) = 3(4x + 8) 4. 2(8x + 10) = 4(4x + 5) 16

17 1. There are 24 cookies on a plate. Jenna and Torri eat n cookies each. How many cookies are left? A. 2n B. 12n C n D. 24 2n 17

18 2. 14 minus a number One less than a number y Sum of four and a number b A number y divided by 40 n students organized into seven equal teams Six more than three times a number m 18

19 3. The number of stamps in Ethan's collection is 4 more than half the number of stamps in Helen's collection. h

20 4. The number of pledges that Melissa collected for this year's charity walk is 8 less than half the number of pledges she collected last year. She collected p pledges last year. Which expression represents the number of pledges she collected this year? A. 2p 8 C. p 8 B. p 8p 2 2 D. 8 p 2 20

21 5. Diego has 60 CDs. This is 12 more CDs than Heidi has. How many CDs does Heidi have? 21

22 6. Simon has six less than 2/3 of the number of baseball cards that Manuel has. Simon has 14 baseball cards. How many cards does Manuel have? 22

23 7. A taxi charges $2.50 for each ride plus $1.25 per mile traveled. If the total charge for one ride was $8.75, how many miles were traveled? 23