Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.
Solve an absolute-value equation by splitting it into two linear cases
Problem
Solve the absolute-value equation \(|x~-~3|~=~5\).
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What this problem is really about
Absolute value describes distance, so a positive target places possible values on both sides of a center. We’ll set the expression inside the bars equal to the positive target and its negative counterpart, solve the two linear cases independently, and keep both branches distinct. Substitution into the original equation confirms that each candidate has the required distance.
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