Question

1. Resolva, em ℝ, as inequações:

a) |3 −4| ≤ 1

b) |− +1| > 1/2

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Answer 1

1.

a)

|3x-4| <= 1

[√(3x-4)² ]²<=1²

(3x-4)² <=1

9x²-24x+16 <=1     ..a=9>0  concavidade p/cima

9x²-24x+15 <=0

x'=[24+√(576-540)]/18=(24+6)/18=30/18=5/3

x''=[24-√(576-540)]/18=(24-6)/18=1

1 ≤ x ≤ 1/3

b)

|-x+1|>1/2

[√(-x+1)²]² >1/2²

(-x+1)² >1/4

x²-2x+1 >1/4

x²-2x+3/4 >0      ...a=1>0  concavidade p/cima

x'=[2+√(4-3)]/2 =(2+1)/2=3/2

x-'=[2-√(4-3)]/2 =(2-1)/2=1/2

(-∞ , 1/2) U (3/2 ,+ ∞ )