uligheder

-2x-7 > 5x+21 <=>

-7-21 > 5x+2x <=>

-28 > 7x <=>

x < -4

2)

-3x < 5 <=>

x > 5/-3

3)

(-1/2)x > -3 <=>

-(1/2)x*-2 < -3*-2 <=>

x < 6

4)

(1/2)x-5 > 3x+15 <=>

(1/2)x*2-10 > 6x+30 <=>

-10-30 > 6x-x <=>

-40 > 5x <=>

x < -8

5)

-4x+12 < 5x <=>

12 < 9x <=>
4 < 3x <=>

x > 4/3

6)

(1/2)x > -(1/3)x <=>
(1/2)x + (1/3)x > 0 <=>
(5/6)x > 0 <=>
x > 0/(5/6) <=>
x > 0

7)

(1/2)(x-1) > 3(2-x)+x <=>

(1/2)x-(1/2) > 6-3x+x <=>

(1/2)x*2-(1/2)*2 > 6*2-3x*2+x*2 <=>

x-1 > 12-6x+2x <=>

x+6x-2x > 12+1 <=>

5x > 13 <=>

x > 13/5

8)

2(x+2)(x-8) > (x+3)(2x+4) <=>

2(x^2-8x+2x-16) > (2x^2+4x+6x+12 <=>

2x^2-16x+4x-32 > 2x^2+4x+6x+12 <=>

2x^2-2x^2-16x+4x-4x-6x > 12+32 <=>

-22x > 44 <=>

x < 44/-22 <=>

x < -2

334)

1)

-1 < x-3 ^ x-3 < 5

A: -1 < x-3 og B: x-3 < 5

-1 < x-3 <=>

A: x > 2

x-3 < 5 <=>

B: x < 8

2)

2x-3 > 3 ^ 3 > -x

A: 2x-3 > 3 og B: 3 > -x

2x-3 > 3 <=>

2x > 6 <=>

A: x > 3

3 > -x <=>

B: x > -3

3)

-x+1 > 2x+2 v x+3 < 5

-x+1 > 2x+2 <=>

-x-2x > 2-1 <=>

-3x > 1
x < -1/3

x+3 < 5 <=>

x < 2

4)

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

A: x < 3x+2 og B: -(1/2)x < 4
x < 3x+2 <=>

-2 < 3x-x

-2 < 2x

A: x > -1

-(1/2)x < 4 <=>

-(1/2)x*-2 > -8 <=>

B: x > -8
 

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