WEBVTT

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Here is the problem: x minus 8 greater than 7.

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Solve the inequality and give the answer in interval notation.

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Move everything to one side and isolate the variable. Collect terms: x minus 15 greater than 0.

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Test one point in each interval (sign chart). (-∞, 15): test x equals 14 → sign minus → excluded; (15, ∞): test x equals 16 → sign plus → included.

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Decide the endpoints. 15: excluded.

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Write the solution set.

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So the answer is (15, ∞).

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The inequality holds exactly for x in (15, ∞). Points where the expression is undefined are never included, and endpoints are included only for less than or equal to or greater than or equal to where the expression equals zero.

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x equals 14: does not satisfy the inequality.

10
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x equals 16: satisfies the inequality.