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Absolute Value Inequalities: Greater Than

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State

For positive k, the inequality |X| > k means X < −k or X > k: the inside expression sits farther than k from zero, on either side.

Show

|x| > 5 splits into x < −5 or x > 5 — two rays, written (−∞, −5) ∪ (5, ∞).

Watch for

Less-than traps; greater-than banishes.

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