Question

me ajudem a resolver essas inequacoes??? agradeço desde já :)

Answer 1

A) 6x + 30 < x - 5
6x - x < - 35
5x < - 35
x < - 35/5
x < - 7

S = {x ∈ Z/ x < - 7}


B) 9x - 2 ≥ 3x + 4
9x - 3x ≥ 6
6x ≥ 6
x ≥ 1

S = {x ∈ Z/ x ≥ 1}


C) 5 - 3x < x + 13
5 - 13 < 4x
8 < 4x
8/4 < x
2 < x (Ou x > 2)

S= {x ∈ Z/ x > 2}


D) 2 * (x + 8) ≤ 18
2x + 16 ≤ 18
2x ≤ 18 -16
2x ≤ 2
x ≤ 2/2
x ≤ 1

S = {x ∈ Z/ x ≤ 1}


E) 5 - 3 * (x + 8) ≤ x - 11
5 -3x - 24 ≤ x - 11
5 - 3x - 13 ≤ x
- 3x - 8 ≤ x
- 4x ≤ 8
x ≤ 8/-4
x ≤ - 2

S = {X ∈ Z/ x ≤ - 2}



F) 3 * (x - 9) + 5 > 2 * (x-1)
3x - 27 + 5 > 2x - 2
x - 22 > -2
x > 20

S = {x ∈ Z/ x > 20} 



2)

A) 4x - 7 ≥ 3 * (x - 4)
4x - 7 ≥ 3x - 4
x ≥ 3

S = {x ∈ Z/ x ≥ 3}


B) 2 * (x+1) - 3 < -5
2x + 2 - 3 < - 5
2x + 2 < - 8
2x < - 10
x < -10/2
x < -5

S= {x ∈ Z/ x < -5}



C) 5x - 3/2 < 3x - 4/3
5x - 3 * 3 < 3x - 4 * 2
5x - 9 < 3x - 8 
2x < -17
x < -17/2

S = {x ∈ Z/ x < -17/2}



D) 2/3 * x - 5/4 + x > 3/5
2x/3 - 5/4 + x > 3/5
2x - 5/4 + x > 3/5 * 3
2x - 5 + x > 3/5 * 3 * 4
2x - 5 + x * 5 > 3 * 3 * 4
2x - 5x - 5 > 36
-3x > 41
x > 41/-3


S = {x ∈ Z/ x > 41/-3}