Solve the following linear inequations in R

Given








For this inequation to be true, there are two possible cases.


i. x + 5 > 0 and x – 5 > 0


x + 5 – 5 > 0 – 5 and x – 5 + 5 > 0 + 5


x > –5 and x > 5


x (–5, ∞) (5, ∞)


However, (–5, ∞) (5, ∞) = (5, ∞)


Hence, x (5, ∞)


ii. x + 5 < 0 and x – 5 < 0


x + 5 – 5 < 0 – 5 and x – 5 + 5 < 0 + 5


x < –5 and x < 5


x (–∞, –5) (–∞, 5)


However, (–∞, –5) (–∞, 5) = (–∞, –5)


Hence, x (–∞, –5)


Thus, the solution of the given inequation is (–∞, –5) (5, ∞).


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