# Absolute Value Equations

```Absolute Value Equations
Solve for x and explain your reasoning:
1. x  2
2. x  0
3. x  1
4. x   x
Since the absolute value of x can either be positive or negative, we must solve for both
the positive and negative solutions of x in an absolute value equation.
Ex:
x2 5
x2 5
x  2  5
+2 +2
+2 +2
X=7
x = -3
{x: x = 7, -3}
Try it!
1. x  4  3
2. 9  x  4
5. 2 x  6  14
6. 3x  4  7
Process:
1. Remove the absolute value sign.
2. Solve for the positive solution.
3. Solve for the negative solution.
3. 6  x  9
4. x  12  8
ISOLATING ABSOLUTE VALUE EXPRESSIONS
Just like solving for x, we need to isolate the entire absolute value expression before we
can solve.
Ex:
2x  7  5  4
+5 +5
2x  7  9
2x – 7 = 9
+7 +7
2x = 16
2
2
X=8
2x – 7 = -9
+7 +7
2x = -2
2
2
x = -1
Check by plugging each solution back into your original equation.
Examples:
1. 6  x  1  9
2. x  17  9  1
3. 7  4  x  12
4. 3x  2  2  5
5. 4 x  3  4  8
6. 3   2 x  9  10
7. 6   x  5  9
8. 4  5x  8  15
9. 7  3x  10  4
10. 2 3x  7  2  4
Homework: Workbook p. 64, 26-49 EVEN
***EXTRA PRACTICE!***
1. x  9  4
2. x  7  16
3. 2 x  4  6  9
4. 4  x  10  14
5. 10  3x  1  24
6. 2 x  9  15  36
7. 2 x 
1
1  9
2
8. 3 x 
1
 5  17
2
9. 3 4 x  9  2  6
```