Algebra: Chapter 3 Notes

Transcription

1 Algebra Homework: Chapter 3 (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework 16 F 2/21 Sections 3.1 and 3.2: Solving and Graphing One-Step Inequalities Section 3.6: Solving Absolute Value Equations HW#16: Pg. 111: 1, 2 Pg. 126: 1-4, 15-18, 34-43x3 Pg. 132: 7-16x3, Pg. 161: 4, 5, 11, (show checks on this page) 17 M 2/24 Sections 3.3 and 3.4: Solving Multi-Step Inequalities Section 3.6: Solving Absolute Value Equations HW#17: Pg. 112: 3, 4 Pg. 133: 29, 34, 46, 58 Pg. 139: 1-21x4, 56, 61, 64 Pg. 146: 7-19x3 Pg. 161: 6, 10, 12, (show checks on this page) 18 T 2/25 Section 3.5: Compound Inequalities HW#18: Pg. 117: 53 Pg. 146: 14-35x3, 41, 42 Pg. 153: 1-37x3 Pg. 161: 19, 40, 42 (show checks on this page) 19 W 2/26 Section 3.6: Absolute Value Inequalities HW#19: Pg. 117: 54 Pg. 147: 54, 57 Pg. 154: 9, 15, 21, 25 Pg. 161: Chapter 3 Test and Notes Check On Friday 20 Th 2/27 Chapter 3 Review HW#20: Pg. 170: 1-38all Correct Homework Online in PEN Chapter 3 Test and Notes Check Tomorrow Print: Chapter 4 Notes by Monday 21 F 2/28 Chapter 3 Test and Notes Check HW#21: Pg. 122: 8-28 even Pg. 174: 1-18all Print: Chapter 4 Notes by Tomorrow 1

2 Notes #16: Sections 3-1, 3-2, and 3-6 Section 3-1: Inequalities and their graphs A. Identifying Solutions of Inequalities A solution of an inequality is any number that makes the inequality. For example, the solutions of the inequality x < 3 are all: Identifying Solutions by Mental Math Is each number a solution of x 7? Meaning, does the value of x make the inequality? 1.) 9 2.) 14 3.) -5 2 Solution: Solution: Solution: Identifying Solutions by Evaluating Is each number a solution of 6x - 3 > 10? Meaning, does the value of x make the inequality? 4.) 3 5.) 4 Solution: Solution: B. Graphing and Writing Inequalities in One Variable How many solutions are there to an inequality like m < -3.5? Rather than list solutions, you can use a graph to indicate all of the solutions of an inequality. When graphing an inequality on a number line, follow these tips: Always arrange the final inequality so the variable is on the side Label your number so that the number in the solution is in the of the graph Use a for < or > and use a for or Graph to the RIGHT when a or and to the LEFT when a or 6.) x < 3 7.) m -2 8.) c > -2 9.) -4 p 2

3 Write an inequality for each graph. Variable choice may vary. 10.) 11.) 12) 13) Section 3-2: Solving Inequalities Using Addition and Subtraction A. Using Addition and Subtraction to Solve Inequalities **When solving an inequality, you can add and subtract the same number from without changing the inequality sign** Solve the following inequalities, then graph the solutions. 14.) x 3 < ) m 6 > ) y + 5 < ) g

4 18.) 3.8 d ) 12 x 5 20.) 4 7 < c + 21.) x Example (Application) 22.) In order to receive a B in your literature class, you must earn more than 350 points of reading credits. Last week you earned 120 points. This week you earned 90 points. How many more points must you earn to receive a B? Section 3-6: Solving Absolute Value Equations A. Solving Absolute Value Equations What does absolute value mean? Recall that the absolute value of a number is its from zero on a number line. Since absolute value represents, it can never be. What does solving an absolute value equation mean? x = 3 means to find the places on the number line that are away from. Solution: 4

5 x = 3 means to find the places on the number line that are away from. Solution: What does the graph of an absolute value equation look like? The graph of x = 3 is below: Solving Absolute Value Equations: Get the alone Write two equations; one and one Solve for x; expect answers Check both answers by Solve each equation. Check your solution. 1.) x + 5 = 11 2.) 3 n = 15 3.) 3 w 1 2 = 4 4.) m 3 = 5 5.) r = 6 6.) 2 3p = 12 5

6 Notes #17: Sections 3-6, 3-3 and 3-4 Section 3.6: Solving Absolute Value Equations 1.) 2 p + 5 = 11 2.) 2 3x = 9 3.) 3 4x 2 = 6 Section 3-3: Solving Inequalities Using Multiplication and Division When multiplying and dividing the same number to both sides of an inequality, follow these rules: If you multiply or divide by a positive number, leave the inequality sign If you multiply or divide by a negative number, the inequality sign. Explore why: Solve and graph the solution: x 2.) 2t < 8 3.) 0.6 > 0.2n 1.) < 1 2 6

7 k 5.) 4c < 24 4.) > 1 4 Algebra: Chapter 3 Notes 6.) w 7.) 5z 25 8.) 1 > t 9.) y 10.) b 1 3 > 11.) x 12.) z > 3 2 C. Application 13.) Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car s gas tank if it costs $25 each time? 7

8 Section 3-4: Solving Multi-Step Inequalities D. Solving inequalities with variables on one side Sometimes you need to perform two or more steps to solve an inequality. Your goal is still the same: to the variable on the side of the inequality sign. Solve and graph your solution. 14.) 5 + 4b < ) 2 8x > ) 8z 6 < 3z ) 6z 15 < 4z ) 3x + 4(6 x) < 2 19.) 5(-3 + d) 3(3d 2) 20.) 4 m 3 2m ) ( y 3) > y

9 Notes #18: Section 3-5 Section 3-5: Compound Inequalities Two inequalities that are joined by the word or the word form a. A. Solving Compound Inequalities Containing AND What does it mean? A solution of an and compound inequality is any number that makes inequalities true. Example: Find a solution for the following inequality x < 9 and x > 7 How do I write it? You can write an AND compound inequality as a sandwich x -5 and x 7 is the same as. How do I say it? There are two correct ways to say this: 1) x is -5 and to 7. 2) x is -5 and 7. How do I graph it? The solution of this inequality can be expressed with the following graph: Write a compound inequality that represents each situation. Graph the solution. 1.) All real numbers that are at least -2 and at most 4. 2.) All real numbers greater than -2 but less than 9. 3.) The books were priced between $3.50 and $6.00, inclusive. Solve the inequality. Graph the solution. When solving sandwich problems, it is like you now have three sides of the equation 4.) Solve -4 < r ) -6 3x < 15 6.) -3 < 2x

10 B. Solving Compound Inequalities joined by an OR What does it mean? A solution of an or compound inequality is any number that makes inequality true. Example: Find a few solutions for the following inequality x > 3 or x < -2,, How do I write it? You cannot write an or compound inequality as one equation. You must write the solution as inequalities separated by an. How do I say it? There is only one correct way to say this: x is 3 or -2. How do I graph it? The solution of this inequality can be expressed with the following graph: Write a compound inequality that represents each situation. Graph the solution. 7.) All real numbers that are less than 0 or greater 8.) Discounted tickets are available to children than 3. under 7 years old or to adults 65 and older. 9.) Solve and graph the compound inequality 3x+ 2 < -7 or -4x + 5 < 1 10.) Solve and graph the compound inequality 4v + 3 < -1 or -2v + 7 < 1 C. Application 11.) Your test grades in science so far are 83 and 87. What possible grades can you make on your next test to have an average between 85 and 90, inclusive? 10

11 Notes#19: Section 3-6 Section 3-6: Absolute Value Equations and Inequalities A. Solving Absolute Value Inequalities What do absolute value inequalities mean? x 2 means What numbers are 2 units away from zero? Graph the solution: Is this an AND or an OR graph? y 2 means What numbers are 2 units away from zero? Graph the solution: Is this an AND or an OR graph? Solving Absolute Value Inequalities: Get alone Write 2 equations, one and one (SWITCH THE SIGN!) If <, use If >,, use Graph and solve for x (sometimes, put back in sandwich) Solve the absolute value inequalities. Graph your solutions. 1.) d ) k

12 3.) v 3 > 4 4.) y ) 4 x ) 6 < c 2 7.) 2y 3 > 8 8.) 4m 3 = 3 10.) 5 2 y = 3 9.) 2 3 x