Question

Preciso resolver esta inequação

 

-2x < 1 - x < -3x +2

Answer 1

 

 

-2x < 1 - x 

 

-2x + x < 1

 

- x < 1(-1)

 

x> -1 

 

 

1 - x < -3x +2

 

-x +3x < 2 - 1

 

2x < 1

 

x < 1/2

 

 

- 1 < x < 1/2

Answer 2

$<var>-2x < 1 - x < -3x+2</var>$

 

Dividimos as inequações em duas partes, e resolvemos uma de cada vez:

 

$<var>\boxed{-2x < 1 - x} < -3x+2 \\\\ -2x < 1 - x \\\\ -2x+x < 1 \\\\ -x = 1 \ \ \ \times (-1) \\\\ \underline{x > -1}</var>$

 

Segunda parte:

 

$<var>-2x < \boxed{1 - x < -3x+2} \\\\ 1 - x < -3x+2 \\\\ 1-2 < -3x+x \\\\ -1< -2x \ \ \ \times (-1) \\\\ 1 > 2x \\\\ \underline{\frac{1}{2} > x}</var>$

 

$<var>\boxed{\boxed{S = \{-1 < x < \frac{1}{2}\}}}</var>$