WEBVTT

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Here is the problem: negative 9x minus 4 less than 9x plus 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: negative 18x minus 11 less than 0. Dividing by a negative coefficient reverses the inequality sign.

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Test one point in each interval (sign chart). (-∞, negative 11 over 18): test x equals negative 2 → sign plus → excluded; (negative 11 over 18, ∞): test x equals 1 → sign minus → included.

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Decide the endpoints. negative 11 over 18: excluded.

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Write the solution set.

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So the answer is (negative 11 over 18, ∞).

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The inequality holds exactly for x in (negative 11 over 18, ∞). 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 2: does not satisfy the inequality.

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x equals 1: satisfies the inequality.