Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.
Solve an absolute-value equation after isolating the absolute value
Problem
Solve the absolute-value equation \(2|x~-~1|~=~10\) after isolating the absolute-value expression.
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What this problem is really about
The absolute-value expression must be isolated before its two distance cases are created. We’ll first undo the multiplication outside the bars, then equate the inside expression to both signed versions of the resulting positive distance. Solving both branches and checking them in the original equation ensures the outside factor was handled and neither valid candidate was lost.
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