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Example: Solving ∣x∣>4|x| > 4

To solve the specific absolute value inequality ∣x∣>4|x| > 4, apply the corresponding greater than property to translate the expression into the equivalent compound sequence x<−4x < -4 or x>4x > 4. This indicates we are seeking all numbers whose actual distance from zero is strictly greater than 44 units. Graphically on a standard number line, this solution is illustrated by placing open parentheses at the −4-4 and 44 marks to demonstrate exclusion, and clearly shading the two separate regions to the left of −4-4 and to the right of 44. Utilizing formal interval notation, this dual solution set is documented as the union (−∞,−4)∪(4,∞)(-\infty, -4) \cup (4, \infty). Additionally, one can intuitively verify this solution by testing arbitrary values from each section, such as −6-6, 00, and 77.

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Updated 2026-06-03

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