Problem 37 of 7
Solve the absolute-value inequality |x - 2| >= 5 and write the union solution.
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produce two-ray solution set.
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Inequality must be distance greater than or greater than/equal to a positive value, producing two rays.
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Solution
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1. For |x - a| >= b, x is at least b units away from a.
2. Split into x - a <= -b or x - a >= b.
3. Solve both rays.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Bounded interval answer for outside-distance statement.