Question

Resolva as inequações:

A)5(x-2)≤ -2 (x-1)

B) (x+2)+(x+3)+(x+4) ≤ 1

Answer 1

A) 5(x - 2) ≤ -2(x - 1) ⇒ 
5x - 10 ≤ - 2x + 2 ⇒
5x + 2x ≤ 2 + 10 ⇒
7x ≤ 12 ⇒
x ≤ 12/7 

S = {x ∈ R | x ≤ 12/7}



B) (x + 2) + (x + 3) + (x + 4) ≤ 1 ⇒
x + 2 + x + 3 + x + 4 ≤ 1 ⇒
x + x + x ≤ 1 - 2 - 3 - 4 ⇒
3x ≤ - 8 ⇒
x ≤ - 8/3

S = {x ∈ R | x ≤ - 8/3}

Answer 2

a)
5.(x - 2) ≤ -2.(x - 1)
5x - 10 ≤ - 2x + 2
5x + 2x ≤ 2 + 10
7x ≤ 12
x ≤ 12/7

R.: {x ∈ R / x ≤ 12/7}

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b)
(x + 2) + (x + 3) + (x + 4) ≤ 1
x + 2 + x + 3 + x + 4 ≤ 1
3x + 9 ≤ 1
3x ≤ 1 - 9
3x ≤ - 8
x ≤ - 8/3

R.: {x ∈ R / x ≤ - 8/3}