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: 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
If x = a, then x = a or x = - a.
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.

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

6. Ex 1. 2x + 3 = 4

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

8. Solve each absolute value equation. Graph the solution on a calculator. *
Ex 3. x - 3 = 3x + 5
Check the solutions. Do they work?
Graph the solution(s) on a number line.

9. Solve each absolute value equation. Graph the solution on a calculator. *
Ex 4. x – 4 = x + 1

10. III. Absolute Value Inequalities
How to tell the difference between AND and OR statements:
If a > 0 and x < a, then x < a AND x > -a.
If a > 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.

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

12. Ex 1. 5 – 3x < 9

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

15. Homework
Integrated Algebra II- Section 1.8 Level A
Academic Algebra II- Section 1.8 Level B