WEBVTT

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Here is the problem: negative 7x minus 4 greater than equals 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 7x minus 11 greater than or equal to 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 7): test x equals negative 3 → sign plus → included; (negative 11 over 7, ∞): test x equals 0 → sign minus → excluded.

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Decide the endpoints. negative 11 over 7: 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 11 over 7].

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The inequality holds exactly for x in (-∞, negative 11 over 7]. 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 3: satisfies the inequality.

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x equals 0: does not satisfy the inequality.