1. Solving Absolute Value Equations

2. What is Absolute Value?
The absolute value of a number is the number of units it is from zero on the number line.
The symbol |x| represents the absolute value of the number x.

3. Remember: ABSOLUTE VALUE7 -7 7 7

4. We can evaluate expressions that contain absolute value symbols.
Think of the | | bars as grouping symbols.
Evaluate
|9(-2) -3| + 5
|-18 -3| + 5
|-21| + 5
21+ 5=26

5. ABSOLUTE VALUE Equationx 7
What can X equal to make this true? -7 7
x = OR

6. Solving Absolute Value Equations

7. Solving Absolute Value Equations
X+4
=11
=11
=11 or
-X-4
=11
X+4
=11
-X=15
X=7
X=-15

8. Solving Absolute Value Equations
X-8
=17
=17
=17 or
-X+8
=17
X-8
=17
-X=9
X=25
X=-9

9. Equations may also contain absolute value expressions
When solving an equation, isolate the absolute value expression first.
Rewrite the equation as two separate equations.
Solve each equation.

10. More Examples Solve 42 - |x + 3| = 15 -|x + 3| = -27 |x + 3| = 27
Write the two separate equations.
x + 3 = 27 or -(x + 3) = 27
x = x + 3 = -27
y = -30

11. Absolute value is never negative. Therefore, no solution
|3d - 9| + 6 = 0 First isolate the variable by
subtracting 6 from both sides.
|3d - 9| = -6
There is no need to go any further with this problem!
Absolute value is never negative.
Therefore, no solution

12. Your turn:
Solve:
|x - 2| = 7
|5 - x| = 31
| x | - 9 = 21

13. Your turn:
Solve:
38 - | x | = 14
4 - |x - 1| = -5