Question #1671

Solve the inequality: |x + 2| + |2 - x| < 8

Expert's answer

There are 3 domains and equivalent inequalities:

x>=2

x+2+2-x < 8;& & 4< 8;& The solution would be [2, ∞ )

-2 <= x < 2

(x+2) - (2-x) < 8; 2x < 8; & x < 4,& solution [-2, 2)

x < -2

-(x+2) -(2-x) < 8; -4 < 8; solution (-∞ , -2]

Union of these solutions gives (-∞ , ∞ )

x>=2

x+2+2-x < 8;& & 4< 8;& The solution would be [2, ∞ )

-2 <= x < 2

(x+2) - (2-x) < 8; 2x < 8; & x < 4,& solution [-2, 2)

x < -2

-(x+2) -(2-x) < 8; -4 < 8; solution (-∞ , -2]

Union of these solutions gives (-∞ , ∞ )

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