Linear Inequations-10

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Solve |x - 2| ≥ 5

Solution: We know that

|x - a| ≥ r <=> x ≤ a – r, or x ≥ a + r

|x - 2| ≥ 5 <=> x ≤ 2 – 5, or x ≥ 2 + 5

<=>x ≤ -3 or x ≥ 7

<=>x ∈ (-∞, -3] or x ∈ [7, ∞)

<=>x ∈ (-∞, -3] U [7, ∞)

Hence, the solution set of the given inequation is (-∞, -3] U [7, ∞)

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