Question

Решите систему неравенств:

{3x - 2 < 1, 5x + 1
{4 - 2x > x - 2

{Зх – 2 > x + 4
{х– 4 >6x+3​

Answer 1

Ответ:

1)

{3х-2<1,5х+1

{4-2х>х-2

{х<2

{х-4>х-2

{х<2

{х<2

2)

{х<3

{х-4>6х+3

{х<3

{- 7/5

Answer 2

Ответ:

1)

$\left \{ {{3x-2<1,5x+1} \atop {4-2x>x-2}} \right. = \left \{ {{3x-1,5x<1+2} \atop {-2x-x>-2-4}} \right. = \left \{ {{1,5x<3} \atop {-3x>-6}} \right. = \left \{ {{x<2} \atop {x<2}} \right.$

Тогда х ∈ (2; - ∞)

2)

$\left \{ {{3x-2>x+4} \atop {x-4>6x+3}} \right. = \left \{ {{3x-x>4+2} \atop {x-6x>3+4}} \right. = \left \{ {{2x>6} \atop {-5x>7}} \right. = \left \{ {{x>3} \atop { x< - 7/5}} \right.$

Тогда х ∈ ∅