Question

1) Determine os valores de x em R que satisfaçam as seguintes inequações:

a) 2 − 3X > X + 14

b) 3 − X < 5 + X

c) 2X − 18 > 4X − 38


d) 2X + 1 ≤ X + 6

e) X + 3 > −X – 1​

Answer 1

a) 2 − 3X > X + 14 ->

-3x-x > 14-2 ->

-4x > 12 (*-1) -> x negativo então multiplica tudo por -1 para trocar sinal

4x < 12 ->

x < 12/4 ->

x < 3

b) 3 − X < 5 + X ->

-x-x < 5-3 ->

-2x < 2 (*-1) ->

x > 2/2 ->

x > 1

c) 2X − 18 > 4X − 38 ->

2x-4x > -38+18 ->

-2x > -20 (*-1) ->

x < 20/2 ->

x < 10

d) 2X + 1 ≤ X + 6  ->

2x-x ≤ 6-1 ->

x ≤ 5

e) X + 3 > −X – 1​

x+x > -1-3 ->

2x > -4 ->

x > -4/2 ->

x > -2