Precalc0011to0016-page11

Precalc0011to0016-page11 - Solve x 1 = 2 . Solution x 1 = 2...

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(Section 0.11: Solving Equations) 0.11.11 PART F: SOLVING ABSOLUTE VALUE EQUATIONS Solving Absolute Value Equations If d > 0 , then x = d ± x d . If d = 0 , then x = d ± x = 0 ± x = 0 . If d < 0 , then x = d has no solutions. • For example, x = 3 ± x 3 , while x = ± 3 has no solutions. WARNING 14 : Remember that absolute values are never negative . • This method can be extended to u = d , where u is an expression in x or some other variable. Example 8 (Solving an Absolute Value Equation)
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Unformatted text preview: Solve x 1 = 2 . Solution x 1 = 2 x 1 = 2 + case : case: x 1 = 2 x = 3 x 1 = 2 x = 1 The solution set is: 1, 3 { } . Observe that 1 and 3 are the two numbers that lie two units away from 1 on the real number line. This is consistent with our discussion of absolute value and distance in Section 0.4....
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