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Checking Inequality Solutions Using Test Points
After computing the solution to a given inequality, it is highly recommended to verify the mathematical result by manually testing specific sample points. The graphed solution reliably partitions the entire number line into three clear sections (one satisfying section and two non-satisfying outer boundaries). To execute a verification check, deliberately select one arbitrary numerical value from each of these defined sections and systematically substitute it back into the original starting inequality. While verifying three points is not a comprehensive, airtight proof for infinite solution sets, confirming that only the points from the shaded solution region yield true mathematical statements provides robust confidence in the obtained answer.
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