2-1 More on Solving Equations Wednesday, May 26, :22 PM

Transcription

1 2-1 More on Solving Equations Wednesday, May 26, :22 PM Objective: Students will solve basic equations Remember: Algebra is an Arabic word meaning: to "undo" and "balance" Solve: Solve b. Chapter 2 Page 1

2 Zero Products Property: If two things timsed together equal zero, one of the things must be zero Solve: a. b. Chapter 2 Page 2

3 2-2 Using Equations (Word Problems) Wednesday, May 26, :55 PM Objective: Students will translate word problems into algebraic equations and solve WARM UP Write an equation but don't solve 1. a number plus five equals seven 2. the sum of twice the number x and two equals three times x 3. the sum of twenty percent of b and one equals b 4. five more than m equals one half m 5. twice c is 5 less than c Example 1: A 28-foot rope is cut into two pieces. One piece is 3 ft longer than the other. How long are the pieces? Example 2: Five plus twice a number is seven times the number. What's the number? Example 3: The price of a mobile home was cut 11% off to a new price of $48,950. What was the original price? Chapter 2 Page 3

4 Example 4: The sum of two consecutive integers is 35. What are the numbers? YOU TRY!! a. A 23-ft cable is cut into two pieces, one three times as long as the other. How long are the two pieces? b. If seven times a certain number is subtracted from 6, the result is five times the number; what s the number? c. Chris bought a baseball card in By 1985 the value had tripled. Since then, the value has gone up another $30. The card is now worth five times the original value. How much did Chris pay for it in 1975? Chapter 2 Page 4

5 d. A store drops the price of an outfit 25% to a sale price of $93; what was the original price? f. The sum of two consecutive odd integers is 36. What are they? g. Field goals count two points each. In one game, Harold had one less field goal than Gunther. Together they scored 46 points. How many points did each player score? And how many field goals did each player make? BONUSES! Chapter 2 Page 5

6 Chapter 2 Page 6

7 2-3 Solving Formulas Wednesday, May 26, :44 PM Objective: Students will use the laws of algebra to manipulate and rearrange formulas Example 1: Rewrite a formula with 2 variables a) Solve the formula C = 2πr for r b) Find the radius of a circle with a circumference of 44 inches Chapter 2 Page 7

8 Chapter 2 Page 8

9 Example 5: Solve 9x - 4y = 7 for y, then find the value of y when x = -5. Example 6: Solve 2y + xy = 6 for y, then find the value of y when x = -3. Chapter 2 Page 9

10 2-4 Solving Inequalities and 2-6 Compound Inequalities Thursday, May 27, :42 AM Objective: Students will solve and graph inequalities X is "less than" x < "greater than" x > "less than or equal to" x < "greater than or equal to" x > 1. Example 1: Graph simple inequalities x x < < x 1. Example 2: Graph compound inequalities -1 < x < 2 2. x -2 or x > 1 When solving inequalities, you solve them exactly as you would an equation, with ONE exception: if you multiply or divide both sides by a negative number then you must reverse the inequality! 1. Solve and graph the inequality. 5x + 2 > 7x x > x x x - 7 6x Chapter 2 Page 10

11 5. x + 6 > x + 7 Solve an "AND" compound inequality--write answer in set notation Graphs of "and" inequalities will be in one segment x x + 3 > -6 Chapter 2 Page 11

12 Solve an "OR" compound inequality--write answer in set notation Graphs of "or" inequalities will be in two segments going in two directions 1. 3x or 5x x - 1 < -1 or 2x x - 4 < -3 or x x or x + 5 < 3 Chapter 2 Page 12

13 2-5 Using Inequalities (Word Problems) Sunday, August 05, :08 PM Objective: Students will model problems with inequalities and solve Example 1: In a history course there will be three tests. You must get a total score of 270 for an A. You get 91 and 86 on the first two tests. What score on the last test will give you an A? Example 2: On your new job you can be paid in two ways. Plan A: A salary of $1600 per month plus a 4% commission of total sales Plan B: A salary of $1800 per month plus a 6% commission of total sales over $10,000 For what amount of total sales is Plan A better than Plan B, assuming that your total sales are always more than $10,000? You Try! Chapter 2 Page 13

14 a. In a chemistry course with five tests, a total of 400 points is needed to get a B. Your first four test scores are 91, 86, 73 and 79. What must you score on the last test to get a B? b. A painter can be paid in two ways. Plan A is $500 plus $45 per hour Plan B is $55 per hour. Suppose the job takes n hours; for what values of n is Plan A better? Chapter 2 Page 14

15 2-7 Absolute Value Equations and Inequalities Thursday, May 27, :29 AM Objective: Students will solve and graph absolute value equations and inequalities EXAMPLE 1 Solving an absolute value equation--solve and graph 1. x - 5 = x - 10 = x-2 +5 = 10 Chapter 2 Page 15

16 EXAMPLE 2 Solve an inequality 1. 2w - 3 < x + 5 > 13 Chapter 2 Page 16

17 You try these. Solve and graph. 1. 2x + 7 > x x 4 4. x + 2 < 6 Chapter 2 Page 17