Solving absolute value equations Lesson 74 Solving absolute value equations

Absolute value The absolute value of a number is never negative The absolute value of a number n is the distance from n to 0 on a number line An equation that has one or more absolute value expressions is called an absolute value equation. Except for 0, there are always 2 points on a number line with the same absolute value The absolute value of a number is never negative

Absolute value then x = 5 or x = -5 Solution set = 5, -5

Solving equations with absolute value , then (x+2) =6 or (x+2)=-6 x+2 = 6 x+2= -6 -2 -2 -2 -2 x= 4 x = -8 Solution set is 4 and -8

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Isolating the absolute value Solve

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Be careful!!!! The absolute value should not be treated like parentheses

Solving special cases 1) when absolute value is equal to 0 there will only be 1 solution 2) when absolute value is equal to a negative number there is no solution

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solve Absolute value is a distance from 0, so it cannot be equal to a negative number. There is no solution

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