2. 1.8 Solving Absolute Value Equations and Inequalities Objectives: Write, solve, and graph absolute value equations and inequalities in mathematical and real world situations. Standards: 2.8.11.A Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.

3. I. Absolute Value The absolute value of x is the distance from x to 0 on the number line.  -3  =  5  =  -256,000  = 3 5 256000

4. II. Absolute Value Equations Break up the original absolute value equation into 2 equations. One of the equations equals the positive value of the right side and the other equation equals the negative value. If  x  = a, then x = a or x = - a.

5. Solve each absolute value equation. Graph the solution on a calculator. Ex 1.  2x + 3  = 4 check and graph Ex 1.  2x + 3  = 4 check and graph

6. Ex 1.  2x + 3  = 4

7. Solve each absolute value equation. Graph the solution on a calculator. * 1.  3x + 5  = 7 Check and graph 2.  x - 3  = 3x + 5 Check and graph 3.  x – 4  = x + 1 Check and graph

8. III. Absolute Value Inequalities How to tell the difference between AND and OR statements: If a > 0 and  x  -a. If a > 0 and  x  -a. If a > 0 and  x  > a, then x > a OR x 0 and  x  > a, then x > a OR x < -a. Break the original absolute value inequality into 2 inequalities. The first inequality is the same as the original problem, but it does not include the absolute value bars. For the second inequality, flip the inequality sign and change the sign of the number on the right side.

9. Solve the absolute value inequality. Graph the solution on a number line. Ex 1.  5 – 3x  < 9 Ex 1.  5 – 3x  < 9

10. Ex 1.  5 – 3x  < 9

11. Solve the absolute value inequality. Graph the solution on a number line. 1.  5x – 3  < 7 Check and graph 2.  3x – 7  > 1 Check and graph 3.  5x + 2  > 8 Check and graph

13. Homework Homework Integrated Algebra II- Section 1.8 Level A Honors Algebra II- Section 1.8 Level B