WEBVTT

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Here is the problem: x minus 3 less than or equal to negative 7.

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Solve the inequality and give the answer in interval notation.

3
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Move everything to one side and isolate the variable. Collect terms: x plus 4 less than or equal to 0.

4
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Test one point in each interval (sign chart). (-∞, negative 4): test x equals negative 5 → sign minus → included; (negative 4, ∞): test x equals negative 3 → sign plus → excluded.

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Decide the endpoints. negative 4: included (the expression equals 0 and the sign allows equality).

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Write the solution set.

7
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So the answer is (-∞, negative 4].

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The inequality holds exactly for x in (-∞, negative 4]. 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.

9
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x equals negative 5: satisfies the inequality.

10
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x equals negative 3: does not satisfy the inequality.