Name: Block: Unit 2 Inequalities

Transcription

1 Name: Block: Unit 2 Inequalities 2.1 Graphing and Writing Inequalities 2.2 Solving by Adding and Subtracting 2.3 Solving by Multiplying and Dividing 2.4 Solving Two Step and Multi Step Inequalities 2.5 Solving Inequalities with Variables on Both Sides 2.6 Solving Compound Inequalities 2.7 Solving Absolute Value Inequalities 2.1 Graphing and Writing Inequalities Standards: A.REI.3 Objectives: Students will be able to

2 Essential Question: Do Now: Vocabulary: Term Definition Example Inequality Solution of an inequality Identifying Solutions of Inequalities Example 1) Describe the solutions of 3+x<9 in words. Let s test values of x to see when the inequality will be true

3 x 3+x 3+x<9 Solution?. Example 2) Describe the solution of 2p<8 in words. Graphing Inequalities *A closed circle means. *An open circle means. Example 1) Graph b > 3

4 Example 2) Graph x 4 Example 3) Graph y Example 4) Graph a > 2 (3 1 ) Writing an Inequality from a Graph Write an inequality shown by the graph Example 1) Example 2)

5 Example 3) Example 4) Exit Ticket

6 2.2 Solving Inequalities By Adding or Subtracting Standards: A.REI.3 Objectives: Students will be able to Essential Question: Do Now: Let s test this.

7 Using Addition and Subtraction to Solve Inequalities Solve each inequality and graph the solutions. Example 1) x + 9 < 16 Example 2) x 5 3 Example 3) 4 + a 2 Example 4) 3 + y < 10 Example 5) x

8 Real World Applications Example 1) Example 2) Exit Ticket

9 2.3 Solving Inequalities by Multiplying or Dividing Standards: A.CED.1, A.REI.3 Objectives: Students will be able to Essential Question: Do Now: Let s test this out

10 Multiplying or Dividing by a Positive number Just like solving inequalities using addition and subtraction, solving is the same thing as solving equations. Solve the inequalities and graph the solutions. Example 1) 4 x > 16 Example 2) 5 x 1 Example 3) y < 3 2 Example 4) 4.5x 9

11 Multiplying or Dividing by a Negative Number What happens when we multiply or divide both sides of an inequality by a negative number? Solve each inequality and graph the solutions. Example 1) 7 x > 14

12 Example 2) x 3 < 3 Example 3) 3.1x 9.3 Example 4) x 6 1 Exit Ticket

13 2.4 Solving Two Step and Multi Step Inequalities Standards: A.CED.1, A.REI.3 Objectives: Students will be able to Essential Question: Do Now: Solving Two Step and Multi Step inequalities is just like solving two step and multi step equations, but remember that when you multiply or divide by a, you must. Solving Multi Step Inequalities Solve the inequality and graph the solutions. Example 1) v > 53

14 Example 2) 8 v 3 Example 3) 6+n > 2 4 Example 4) 5 + k 8 7 Simplifying before Solving Inequalities Solve each inequality and graph the solutions. Example 1) 90 > 6(b 6 )

15 Example 2) 4(r 7) 20 Example 3) 206 > (5n + 7 ) Example 4) b < 12 5 Exit Ticket

16 2.5 Solving Inequalities with Variables on Both Sides Standards: A.CED.1, A.REI.1, A.REI.3 Objectives: Students will be able to Essential Question: Do Now: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. Example 1) 16 7 r < r

17 Example 2) 4 v + 8 > 8 v Example 3) 3n 10 n + 6 Example 4) 1 2 v < 3 v + 16 Simplifying Each Side Before Solving Solve each inequality and graph the solutions. Example 1) 8 (2 + 6a) 16 6 a Example 2) 4(a 7 ) > 4 a + 34

18 Example 3) 6 x < 6 (3 + 4 x) Example 4) 30 8b 6(5b 6 ) All Real Numbers as Solutions or No Solutions *Some inequalities are true no matter what value is substituted for the variable. For these inequalities, the solution is. *Some inequalities are false no matter what value is substituted for the variable. For these inequalities, there. Solve each inequality. Example 1) x + 5 x + 3

19 Example 2) 2 (x + 3 ) < x Exit Ticket 1.6 Solving Compound Inequalities Standards: A.REI.3 Objectives: Students will be able to Essential Question: Do Now: Vocabulary: Term Definition Example Compound Inequality

20 Intersection Union Solving Compound Inequalities Involving AND Example: We want to graph the solutions of x<10 and x>0. First draw a venn diagram to see some solutions. Then graph the solutions to both inequalities. The intersection of the graph shows the numbers that are. Solve each inequality and graph the solutions. Example 1) 4 x + 2 8

21 Example 2) 2 2 x Example 3) 4 3 n + 5 < 11 Solving Compound Inequalities Involving OR We want to find the solutions for the inequalities x>10 or x<0. First draw a Venn diagram to see the solutions of each inequality. Then graph the solutions of each inequality. The union will show the solutions of. Example 1) 4 + a > 1 or 4 + a < 3

22 Example 2) 2x 6 or 3x > 12 Example 3) 7 x > 21 or 2x < 2 Writing a Compound Inequality from a Graph Example 1) Does this inequality involve AND or OR? Are there open or closed circles? Example 2) Does this inequality involve AND or OR? Are there open or closed circles? Exit Ticket

23 1.7 Solving Absolute Value Inequalities Standards: A.CED.1, A.REI.3 Objectives: Students will be able to Essential Question: Do Now: Solving Absolute Value Inequalities Involving <

24 Solve each inequality and graph the solutions Example 1) x + 3 < 12 Example 2) 7 n < 5 Example 3) 4 b 36

25 Example 4) 5 6n 60 Solving Absolute Value Inequalities Involving > Example 1) a + 7 1

26 Example 2) k 2 2 > 9 Example 3) p 4 > 3 Example 4) 2 x Special Cases of Absolute Value Inequalities *If you get a statement that is true for all values of a variable, are solutions of the original inequality. *If you get a false statement when solving an absolute value inequality, the original inequality > Example 1) x 9 11

27 Example 2) 4 x Exit Ticket Points for Unit Graphing and Writing Inequalities /5 2.2 Solving by Adding and Subtracting /5 2.3 Solving by Multiplying and Dividing /5 2.4 Solving Two Step and Multi Step Inequalities /5

28 2.5 Solving Inequalities with Variables on Both Sides /5 2.6 Solving Compound Inequalities /5 2.7 Solving Absolute Value Inequalities /5 Total /35