MathB65 Ch 1 I,II,III, IV.notebook. August 23, 2017

Transcription

1 Chapter 1: Expressions, Equations and Inequalities I. Variables & Constants II. Algebraic Expressions III. Translations IV. Introduction to Equations V. The Additive/Multiplication Principles VI. Strategy to Solving Linear Equations of 1-Variable VII. Formulas VIII. Problem Solving using Algebra IX. Intervals X. Solving Inequalities XI. Intersections, Unions, & Compound Inequalities 1

2 I. Variables & Constants Definition: A variable is a quantity which can vary or change. Exercise: 1) Let T represent be the temperature in degrees Fahrenheit. What does T = -15 mean in this case? 2) Let t be the number of years since What does t = 10 mean in this situation? Don't forget "units" 2

3 Definition: A constant is a quantity which does not vary or change. Exercise: A rectangle has a given area of 24 square inches. 1) Give three possible rectangles. 2) What is the constant in this exercise? 3) What are the variables in this exercise? 3

4 II. Algebraic Expressions Definition: An algebraic expression consists of variables and/or numerals often with operation signs and grouping symbols. Exercise: The cost to take a particular taxi company in New York City is given by the expression 3 + 2x, where x is the number of miles driven. 1) What is the cost to take a taxi ride for 8 miles? 2) What does the 2x mean in the expression? 3) What does the 3 mean in the expression? 4

5 Exercise: Find the numerical value for the expressions given 5

6 Combining Like Terms When two terms have variable factors that are exactly the same, the terms are called like or. Match the like terms respective powers are identical. 6

7 Exercise: Simplify 7

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9 The Distributive Law: a(b + c) = ab + ac Show that Use distributive law to re-write the following expressions. 9

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12 III. Translations Identify the following key words with one of the symbols Addition Subtraction Multiplication Division Minus Quotient of Added to Ratio of Product of Increased by Decreased by Of Divided by Sum of Subtracted from Multiplied by Divided into More than Less than Per 12

13 1) 5 more than 20 2) 5 less than 20. 3) The difference of 6 and

14 Translate each phrase to an algebraic expression. 1) 9 more than y. 2) 7 less than x. 3) The difference of 7 and x. 4) The product of 3 and twice t. 14

15 5) The sum of three times a number and 7. 6) Three times the sum of a number and 7. 15

16 IV. Introduction to Equations An equation you should know! Find the area of a triangle where the base is 12 inches and height is 7.2 inches. 16

17 When two algebraic expressions have an equal symbol, =, between them, then the sentence is an Question: Which of the following is an equations and which is an expression? What if we x + 12 = 21 17

18 Definition: of an equation is a replacement of the variable(s) that make the equation true. Question: is 4 a solution of x + 12 = 21? Question: is 9 a solution of x + 12 = 21? Definition: solve an equation means to find all of its solutions. 18

19 Exercise: Determine if the given number is a solution to the equation. 19

20 Words that translate into equality (=): "Is the same as" "The result is" Translate the problem into an equation. 1) What number increased by 5 is 120? 2) When we take twice a number, the result is 50. 3) The differenct of a number and five is the same as twice the number. 20

21 Chapter 1 Homework Part I: Variables & Constants 1) Let n be the number (in thousands) registered at Bakersfield College. What does n = 12 mean in this situation? 2) Let c be the cost (in dollars) to mail a package from the post office. What does c = 5.62 mean in this situation? 3) The perimeter of a rectangle is the sum of all its four sides. A particular rectangle has a fixed perimeter of 100 feet. a) Give two different rectangles that fit this description. b) What are the variables in this situation? c) What are the constants in this situation? 21

22 Part II: Algebraic Expressions Evaluate the given expression for the given value of the variable. Simplify each algebraic expression. 22

23 Part III: Translations Write the following as a algebraic expression. 15) The sum of five and a number 16) The product of a number and 10 17) The difference of 10 and a number Part IV: Introduction to Equations Determine if the given number is a solution to the equation. 23

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