WEBVTT

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Here is the problem: 2x plus 9 less than x minus 8.

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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 plus 17 less than 0.

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Test one point in each interval (sign chart). (-∞, negative 17): test x equals negative 18 → sign minus → included; (negative 17, ∞): test x equals negative 16 → sign plus → excluded.

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Decide the endpoints. negative 17: excluded.

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Write the solution set.

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So the answer is (-∞, negative 17).

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The inequality holds exactly for x in (-∞, negative 17). 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 negative 18: satisfies the inequality.

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x equals negative 16: does not satisfy the inequality.