Question

$encontre \: o \: valor \: de \: x$

a) 9

b) 8

c) 10

d) 15​

Answer 1

Resposta:

c) 10

Explicação passo-a-passo:

$\frac{4x + 8}{4x - 8} = \frac{4x + 20}{4x}$

$\frac{4(x + 2)}{4(x -2) } = \frac{4(x + 5)}{4x}$

$\frac{x + 2}{x - 2} = \frac{x + 5}{x}$

$(x + 2)x = (x + 5)(x - 2)$

$x {}^{2} + 2x = x {}^{2} - 2x + 5x - 10$

$x {}^{2} - x {}^{2} + 2x =- 2x + 5x - 10$

$2x = 3x - 10$

$- 3x + 2x = - 10$

$- x = - 10 \: ( - 1)$

$x = 10$

Answer 2

$\large\boxed{\begin{array}{l} \sf\dfrac{4x + 8}{4x - 8} = \dfrac{4x + 20}{4x} \\ \\ \sf \dfrac{4(x + 2)}{4(x - 2) } = \dfrac{4(x + 5)}{4x} \\ \\ \sf \dfrac{x + 2}{x - 2} = \dfrac{x + 5}{x} \\ \\ \sf (x + 2) \: . \: x = (x + 5) \: . \: (x - 2) \\ \\ \sf x {}^{2} + 2x = x {}^{2} - 2x + 5x - 10 \\ \\ \sf 2x = - 2x + 5x - 10 \\ \\ \sf 2x = 3x - 10 \\ \\ \sf 2x - 3x = - 10 \\ \\ \sf - x = - 10 \\ \\ \sf x = \dfrac{ - 10}{ - 1} \\ \\ \boxed{ \boxed{ \sf{x = 10}}} \leftarrow \textsf{Letra C}\end{array}}$