Absolute Value Notes and Worksheets - Lindsay Bowden - Free Printable

- absolute value – the distance of a number from zero; the absolute value of a number is always non-negative
- example: |5| = 5, |-7| = 7

Solving |x + 3| + 4 = 9:
- STEP 1: Isolate the absolute value expression → |x + 3| = 5
- STEP 2: Write the equation twice with positive and negative answers → x + 3 = 5 and x + 3 = -5
- STEP 3: Solve both equations → x = 2 and x = -8

Examples:
1. |2x - 1| = 11
- 2x - 1 = 11 → 2x = 12 → x = 6
- 2x - 1 = -11 → 2x = -10 → x = -5
- Solutions: x = 6, x = -5

2. |4x| = 16
- 4x = 16 → x = 4
- 4x = -16 → x = -4
- Solutions: x = 4, x = -4

3. |x + 4| - 10 = 3
- |x + 4| = 13
- x + 4 = 13 → x = 9
- x + 4 = -13 → x = -17
- Solutions: x = 9, x = -17

4. |x| - 2 = 16
- |x| = 18
- x = 18
- x = -18
- Solutions: x = 18, x = -18

5. |x| = -5
- No solution (absolute value cannot be negative)

6. |x/5| + 2 = 6
- |x/5| = 4
- x/5 = 4 → x = 20
- x/5 = -4 → x = -20
- Solutions: x = 20, x = -20