Question

Determine o conjunto solução de cada inequação 

a) (x-3) . (2-x) > 0
b) (3x-6) . (2-4x) > 0
c) (-x+2) . (-3x-9) < 0

Answer 1

Olá Rafaela!

Para resolver as inequções do 1 grau é só igualar cada uma delas a 0 e determinar o intervalo...

$x-3>0 \\ x>3 \\ \\ 2-x>0 \\ -x>-2*(-1) \\ x<2$
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Letra A....$S=]2,3[$

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$3x-6>0 \\ 3x>6 \\ x>6/3 \\ x>2 \\ \\ 2-4x>0 \\ -4x>-2*(-1) \\ 4x<2 \\ x< \frac{1}{2}$

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Letra B..$S=] \frac{1}{2},2 [$

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$-x+2<0 \\ -x<-2*(-1) \\ x>2 \\ \\ -3x-9<0 \\ -3x<9 \\ -x<9/3 \\ -x<3*(-1) \\ x>-3$

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Letra C...$S=]-3,2[$