1Cademy - Try It: Solving $$3|x - 4| - 4 = 8$$ and $$2|x

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Example: Solving Absolute Value Equations Requiring Isolation

Example

Try It: Solving $3|x - 4| - 4 = 8$ and $2|x - 5| + 3 = 9$

To practice isolating absolute value expressions with a coefficient, solve the equations $3|x - 4| - 4 = 8$ and $2|x - 5| + 3 = 9$ . For the first equation, add $4$ to both sides to get $3|x - 4| = 12$ , then divide by $3$ to find $|x - 4| = 4$ . The equivalent equations are $x - 4 = -4$ or $x - 4 = 4$ , which solve to $x = 0$ or $x = 8$ . For the second equation, subtract $3$ from both sides to obtain $2|x - 5| = 6$ , then divide by $2$ to yield $|x - 5| = 3$ . The equivalent equations $x - 5 = -3$ or $x - 5 = 3$ solve to $x = 2$ or $x = 8$ .