1. 3-6 Solving Equations Involving Absolute Value (1 st ½ of Lesson) 3-6 Solving Equations Involving Absolute Value (1st ½ of Lesson) Objectives: To solve equations involving absolute value

2. What is absolute value? The distance from zero on the number line. Every absolute value has two solutions…ex. |-2| = 2 and |2| = 2 because both are two spaces from zero on the number line. EVERYONE OF YOUR ABSOLUTE VALUE PROBLEMS MUST HAVE 2 ANSWERS!!!

3. Example 1 Solve. y = 3or y = -3

4. Example 2 Solve. -5 x = 7or x = -7

5. Example 3 Solve. -3 55

6. Example 4 What to do when you have something INSIDE the absolute value. 2 |d + 3| = 8 Divide by 2 |d + 3| = 4 Now, keep in mind you have a positive answer and a negative answer. So… d+3 = 4 OR d+3 = -4 -3 = -3 - 3 -3 d = 1 d = -7

7. 1) Solve these on your paper then see if your neighbor has the same thing. I’m going to call on a pair of you to come work these out. 2) 3) 4) 2|x+3| +3 = 7

8. 1) Solve these on your paper then see if your neighbor has the same thing. I’m going to call on a pair of you to come work these out. 2) 3) 4) 2|x+3| +3 = 7 y = 17 & -17 y = 6 & -6 y = 7 & -7 y = -1 & -5

9. 3-6 Solving Inequalities Involving Absolute Value (2 nd ½ of Lesson) 3-6 Solving Inequalities Involving Absolute Value (2nd ½ of Lesson) Objectives: To solve inequalities involving absolute value

10. Let’s Review a Bit… We know that absolute value equations always have TWO answers. So an absolute value inequality will always have TWO inequalities. When you have two inequalities smushed together into one problem, what is that called? compound inequality There are two types of compound inequalities: AND and OR So then absolute value inequalities are either an AND or an OR. How do you tell the difference?

11. AND or OR? ● If you have a < or ≤ you are working with an ‘and’ statement. Remember: “Less thand” ● If you have a > or ≥ you are working with an ‘or’ statement. Remember: “Greator”

12. Examples ● |2x + 1| > 7 ● 2x + 1 >7 or 2x + 1 < -7 ● -1 > -1 or -1 -1 ● 2x > 6 or 2x < -8 ● x > 3 or x < -4 This is an ‘or’ statement. (Greator). Rewrite. Remember, absolute values are to the right (+) and to the left (-) of zero! Solve each inequality. Graph the solution. 3 -4

13. Examples ● |x -5|< 3 ● x -5 -3 ● x – 5 -3 ● +5 +5 +5 +5 ● x 2 or you can rewrite as 2 < x < 8 This is an ‘and’ statement. (Less thand). Rewrite. Remember, absolute values are to the right (+) and to the left (-) of zero! Solve each inequality. Graph the solution. 8 2

14. So…let’s see if you know today’s lesson. 1.How many answers do absolute value equations have? 2 2.How many answers do absolute value inequalities have? infinite 3.How do you know if an absolute value inequality is an OR problem? > or > 4. How do you know if an absolute value inequality is an AND problem? < or < Now, check your post-it with your neighbors. Did you get the questions right? These are your basic notes all summed up on one post-it.

15. Pg. 170 30. |2y-3| ≥ 7 This is a greatOR problem 2y-3 ≥ 7 OR 2y-3 < -7 2y – 3 ≥ 7 OR 2y - 3 < -7 +3 +3 +3 +3 2y ≥ 10 OR 2y < -4 y ≥ 5 OR y ≤ -2 Don’t forget to graph it! Pg. 170 27. |y-2| ≤ 1 This is a lessAND problem y-2 -1 y – 2 1 +2 +2 +2 +2 y 1 -1 < y < 3 Don’t forget to graph it! Solve these on your paper then see if your neighbor has the same thing.