Question

3) Resolva as seguintes inequações em R:

a) 2(x + 3) > 3 (1 - x)


b) 3(1 - 2x) < 2(x + 1) + x - 7


c) x/3 - (x+1)/2 < (1 - x) / 4


d) (x + 3) > (-x-1)


e) [1 - 2*(x-1)] < 2


f) 6x + 3 < 3x + 18


g) 8(x + 3) > 12 (1 - x)


h) (x + 10) > ( -x +6)

Answer 1

a) 2x + 6 > 3 - 3x

2x - 2x + 6 > 3 - 3x - 2x

6 - 3 > -5x

3 > - 5x

-x < 3/5

x > -3/5

b)3 - 6x < 2x + 2 + x - 7

-6x - 3x < -8

-9x < -8

9x > 8

x > 8/9

c) 4x/12 __ 6* (x + 1)/12 < 3*(1 - x)/12

4x - 6r - 6/12 < 3 - 3x/12

-2x - 6 < 3 - 3x

x < 9

d) x + 3 > -x - 1

2x > -4

x > -4/2

x > -2

e)1 - 2x + 2 < 2

- 2x < 2 - 1 - 2

- 2x < -1

2x > 1

x > 1/2

f) 6x - 3x < 18 - 3

3x < 15

x < 15/3

x < 5

g) 8x + 24 > 12 - 12x

20x > 12 - 24

20x > -12

x > -12/20

x > -3/5

h) x + x > 6 - 10

2x > -4

x > -4/2

x > -2

Answer 2

Olá:
vamos aos cálculos:

a) 2(x + 3) > 3 (1 - x)
2x + 6 > 3 - 3x
5x > -3
x > -3/5

b) 3(1 - 2x) < 2(x + 1) + x - 7
3 - 6x < 2x + 2 + x - 7
-9x < -8
9x > 8
x > 8/9

c) x/3 - (x+1)/2 < (1 - x) / 4
4x/12 - 6* (x + 1)/12 < 3*(1 - x)/12
4x - 6x -6 < 3 - 3x
x < 9

d) (x + 3) > (-x-1)
2x > -4
x > -4/2
x > -2

e) [1 - 2*(x-1)] < 2
1 - 2x + 2 < 2
- 2x < -1
2x > 1
x > 1/2

f) 6x + 3 < 3x + 18
3x < 15
x < 15/3
x < 5

g) 8(x + 3) > 12 (1 - x)
8x + 24 > 12 - 12x
20x > -12
x > -12/20
x > -3/5

h) (x + 10) > ( -x +6)
2x > -4
x > -4/2
x > -2