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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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Solving Absolute Value Equations

The equation in the next example involves absolute value.

Example 1

Solving an absolute value equation by factoring

Solve | x2 - 2x - 16 | = 8.

Solution

First write an equivalent compound equation without absolute value:

 x2 - 2x - 16 = 8 or x2 - 2x - 16 = -8 x2 - 2x - 24 = 0 or x2 - 2x - 8 = 0 (x - 6)(x + 4) = 0 or (x - 4)(x + 2) = 0 x - 6 = 0 or x + 4 = 0 or x - 4 = 0 or x + 2 = 0 x = 6 or x = -4 or x = 4 or x = -2

The solution set is {-2, -4, 4, 6}. Check each solution.