WEBVTT

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Here is the problem: 7x plus 4 less than equals 6x minus 9.

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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 13 less than or equal to 0.

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Test one point in each interval (sign chart). (-∞, negative 13): test x equals negative 14 → sign minus → included; (negative 13, ∞): test x equals negative 12 → sign plus → excluded.

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Decide the endpoints. negative 13: included (the expression equals 0 and the sign allows equality).

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Write the solution set.

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So the answer is (-∞, negative 13].

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The inequality holds exactly for x in (-∞, negative 13]. 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 14: satisfies the inequality.

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x equals negative 12: does not satisfy the inequality.