1. 1.7 Solve Absolute Value Equations and Inequalities
Chapter 1
1.7 Solve Absolute Value Equations and Inequalities
Prepared by Donald Danner

2. In this lesson you will:
Solve absolute value expression and inequalities.
Use absolute value equations and inequalites to solve real-life problems.

3. The absolute value of a number x (written |x| or abs(x))
Chapter 1
The absolute value of a number x (written |x| or abs(x))
Is the distance the number is from 0 on a number line. It is always a non-negative value.
The distance between -4 and 0 is 4, so |-4|=4
The distance between 4 and 0 is 4, so |4|=4
What is the |0|=?
Prepared by Donald Danner

4. Solving an Absolute Value Equation
Chapter 1
Solving an Absolute Value Equation
The absolute value equation |ax+b|=c, where c>0, is equivalent to the compound statement ax+b=c or ax+b=-c
Prepared by Donald Danner

5. Solve |2x – 5| = 9 2x – 5 = 9 2x-5 = - 9 2x = 14 2x = -4 x = 7 x = -2
Chapter 1
Solve |2x – 5| = 9
And
2x – 5 = 9
2x-5 = - 9
2x = 14
2x = -4
x = 7
x = -2
Check these two solutions by substituting into the original equation.
|2(7)-5|=|9|=9
|2(-2)-5|=|-9|=9
Prepared by Donald Danner

6. An absolute value inequality such as |x-1|<3
Chapter 1
An absolute value inequality such as |x-1|<3
Can be solved by rewriting it as a compound inequality -3 < x – 1 < 3
The solutions for x are any number between -2 and 4 not including the numbers -2 and 4…….Notice that is the numbers 3 units to the left of 1 and 3 units to the right of 1.
-2 < x < 4
Prepared by Donald Danner

7. Solve |3x – 2| > 8 -8 > 3x – 2 > 8 -6 > 3x > 10
Chapter 1
Solve |3x – 2| > 8
-8 > 3x – 2 > 8
-6 > 3x > 10
-2 > x > 10/3
Carefully read what this is saying!
As you can see, this is the same as the compound statement a x < -2 OR x > 10/3.
Prepared by Donald Danner