WEBVTT

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Here is the problem: |x minus 1| less than negative 2.

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Solve an absolute value inequality by turning it into a compound inequality and finding the boundary points.

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Write the problem with the absolute value isolated. The absolute value is already alone on one side, so it can be split into cases.

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Compare the right-hand side with zero. An absolute value is never negative, so it cannot be less than a number that is zero or negative.

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Write the solution set in interval notation.

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So the answer is No solution; interval notation: ∅.

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An absolute value inequality compares a distance with c: "less than" keeps the inside within c of zero (one interval), "greater than" pushes it beyond c (two rays).