Question

Determine o conjunto Universo (U) e o conjunto solução (S) das seguintes equações:
a) 6(2x + 4) = 2(3x + 6)
b) x(x – 4) + 81 = 2x(x – 2)
c)

Answer 1

Explicação passo-a-passo:

a)

$\sf 6(2x+4)=2(3x+6)$

$\sf 12x + 24 = 6x + 12$

$\sf 12 x -6x =12-24$

$\sf 6x = -12$

$\sf x =\frac {-12}{6}$

$\sf x = -2$

b)

$\sf x(x-4)+81=2x(x-2)$

$\sf x^2-4x+81=2x^2-4x$

$\sf x^2 -4x + 81 -2x^2+4x = 0$

$\sf -x^2+81 =0$

$\sf x^2 = 81$

$\sf x = \sqrt{81}$

$\sf x = 9$

c)

$\sf \frac{x+3}{3-x} -1=\frac{x}{3-x}$

$\sf \frac{x+3}{3-x} -\frac{x}{3-x} =1$

$\sf \frac{x+3-x}{3-x} =1$

$\sf \frac{3}{3-x} =1$

$\sf 3=3-x$

$\sf x= 3-3$

$\sf x=0$

Espero ter ajudado !!!

Answer 2

Resposta:

OLÁ

VAMOS A SUA PERGUNTA:⇒⇒

A:====>

$\sf 6(2x+4)=2(3x+6)$

$\sf 12x+24=2(3x+6)$

$\sf 12x+24=6x+12$

$\sf 12x+24-6x=12$

$\sf 6x+24=12$

$\sf 6x=12-24$

$\sf 6x=-12$

$\sf x=\dfrac{-12}{6}$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \red{x=-2}}}}\ \checkmark$

B:====>

$\sf x(x-4)+81=2x(x-2)$

$\sf x^2-4x+81=2x(x-2)$

$\sf x^2-4x+81=2x^2-4x$

$\sf \sf x^2-4x+81-2x^2=-4x$

$\sf -x^2-4x+81=-4x$

$\sf -x^2-4x+81+4x=0$

$\sf -x^2+81=0$

$\sf -x^2=-81$

$\sf x^2=\dfrac{-81}{-1}$

$\sf x^2=81$

• Calcule a raiz quadrada de ambos os lados da equação.

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \green{x=9} }}}\ \checkmark\\\\\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \orange{x=-9}}}}\ \checkmark$

C:====>

$\sf \dfrac{x+3}{3-x}-1= \dfrac{x}{3-x}$

$\sf x+3+(-x+3)(-1)=x$

$\sf x+3+x-3=x$

$\sf 2x+3-3=x$

$\sf 2x=x$

$\sf 2x-x=0$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \green{x=0}}}}\ \checkmark$

Explicação passo-a-passo:

ESPERO TER AJUDADO