ABSOLUTE+VALUE+EQUATION+AND+INEQUALITIES

Absolute Value Equations

To solve absolute values:
 * 1) Isolate the absolute value
 * 2) Split using "OR"
 * 3) Solve both parts
 * 4) Test in original equation

Solve: I x-3 I = 6 Isolate: I x-3 I = 6 Split using "OR": x-3 = 6 or x-3 = -6 Solve both parts: x = 9 or x = -3 Test in original equation: I 9 -3 I =6 ::::::: I -3 -3 I = -6 6 = 6 ::::::::::::: 6 = 6

I 4x-3 I = 8 4x-3 = 8 or 4x-3 = -8 4x = 11 or 4x = -5 x = 11/4 or x = -5/4
 * 1.** 8 I 4x-3 I = 8

2 I x-3 I = -4 I x-3 I = -2 x-3 = -2 or x-3 = 2 x = 1 or x = 5 does not equal
 * 2.** 2 I x-3 I +7 = 3

3 I x+6 I = 9x -6 I x+6 I = 3x-2 x+6 = 3x-2 or x+6 = -3x+2 8 = 2x or 4x = -4 4 = x or x = -1 x = 4
 * 3.** 3 I x+6 I +2 = 9x-4

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