Algebra II A Guided Notes

Transcription

1 Algebra II A Guided Notes Name Chapter 1 Period Notes 1-5 Learning Matrix Goal #9: I can solve inequalities. Learning Matrix Goal #10: I can solve real-world problems involving inequalities. Learning Matrix Goal #11: I can write solutions in set notation. Learning Matrix Goal #12: I can write solutions in interval notation. How can inequalities be used to compare phone plans? If Kuni knows that she will use no more than 150 minutes per month, which plan is best for her? How much would she pay if she used 350 minutes under Plan 1? under Plan 2? Key Concept Addition Property of Inequality Properties of Inequality Example Subtraction Property of Inequality Example Now take notes from Khan Academy. Go to Math Then Algebra Then Linear Inequalities Then Thinking Algebraically About Inequalities Then watch the video called One-Step Inequality Involving Addition (that exact title) x + 8 6

2 Example 1 Solve an Inequality Using Addition or Subtraction Solve 7x 5 > 6x + 4 Graph the solution set on a number line. Your Turn Solve 4y 3 < 5y + 2. Graph the solution set on a number line. In both the boxes below, highlight the case where c is negative. Key Concept Multiplication Property of Inequality Properties of Inequalities Examples

3 Division Property of Inequality Examples EXPLAIN THE IDEA THAT IS HAPPENING FOR THE CASES WHEN c IS NEGATIVE FROM THE ABOVE BOXES this is an important idea Reading Math (set notation) {x x>9} is read is greater than 9 Now take notes from Khan Academy. Go to Math Then Algebra Then Linear Inequalities Then Thinking Algebraically About Inequalities Then watch the video called inequalities Using Multiplication and Division (that exact title) -0.5x x 125 (5:11) (8:45)

4 Example 2 Solve an Inequality Using Multiplication or Division Solve -0.25y 2. Graph the solution set on a number line Your Turn Solve p. Graph the solution set on a number line Reading Math (Infinity) The symbol + is read positive, and the symbol - is read negative. The solution set of an inequality can also be described by using interval notation. The infinity symbols are used to indicate that a set is in the positive or negative direction. To indicate that an endpoint is not included in the set, a is used. x < 2 Interval notation (-, 2) Graph Below: A is used to indicate that the endpoint, -2 is included in the solution set. Parenthesis are always used with the symbols + and -, because they do not include endpoints. x -2 Interval notation [-2, + ) Graph Below:

5 WATCH THE VIDEO ON SET AND INTERVAL NOTATION Click the link from the agenda on the website and take notes on a separate sheet of paper. Attach them to these notes. WRITE DOWN EVERYTHING THAT I WRITE DOWN. Now take notes from Khan Academy. Go to Math Then Algebra Then Linear Inequalities Then Thinking Algebraically About Inequalities Then watch the video called Mulit-Step Inequalities (that exact title) 4x + 3 < -1 5x > 8x + 27 (1:27) 8x 5(4x +1) (4x 3) (3:47)

6 Example 3 Solve a Multi-step Inequality Solve m. Graph the solution set on a number line. Your Turn Solve x. Graph the solution set on a number line. Study Tip When solving an inequality, if you arrive at a false statement, such as 3 > 5, then the solution set for that inequality is the, When solving an inequality, if you arrive at a true statement such as 3 > -1, then the solution set for that inequality is the set of. AND IS SYMBOLIZED BY -get this from the board Example 4 Write an Inequality Craig is delivering boxes of paper to each floor of an office building. Each box weighs 64 pounds, and Craig weighs 160 pounds. If the maximum capacity of the elevator is 2000 pounds, how many boxes can Craig safely take on each elevator trip? Explore

7 Plan Solve Examine REVIEW IN YOUR OWN WORDS Name four different ways to show the solution of an inequality How do we know when to reverse the inequality sign? How do we know when to use an open circle in a line graph? Closed circle? Now complete page 37 #1-3, odd, 11, 39, 40. Then from #41-46 choose 2. Also choose either 48 & 49 or 50 & 51. Be sure to answer in both set and interval notation. When assignment is complete, you should check your solutions (get them from the solutions folder). Mark correct problems with a star. Mark incorrect problems with an X and them make corrections on the problems that you had incorrect.