Question

Determine os valores de x nos casos abaixo: a) (2x – 12 ) . ( x – 8 ) ≥ 0 b) ( - x + 3 ) : ( 3x + 3) < 0

Answer 1

Resposta:

Explicação passo-a-passo:

(2x – 12 ) . ( x – 8 ) ≥ 0

2x.x +2x.(-8) -12.x -12(-8)≥0

2x² -16x -12x +96≥0

2x² -28x+96≥0

Δ= (-28)²-4(2)(96)

Δ=784 -768

Δ=16

x≥-(28)±√16/ 2.2

x≥ -28±4/4

x≥-28+4/4 → x≥-24/4 → x≥ -6

x≥ -28-4 /4 →x≥ -32/4  → x≥ - 8

b) ( - x + 3 ) : ( 3x + 3) < 0

-x(3x) -x(3) +3(3x) +3(3) <0

-3x² -3x+9x +9<0

-3x² +6x +9<0

Δ=6² -4(-3)(9)

Δ= 36 +108

Δ=144

x< -6 ±√144/2(-3)

x< -6 ±12/-6

x<-6+12/-6 →x< 6/-6 → x<-1

x<-6-12/-6 → x<-18/-6 → x< 3