Question

Determine x na igualdade (14/x)=(14/2x+10)

Answer 1

☺ Olá ☺

❑ Vamos determinar x :

Nós damos ☞ $\dfrac{14}{x} = \dfrac{14}{2x} + 10$.

■ $\dfrac{14}{x} = \dfrac{14 + 20x}{2x}$

■ $28x = 14x + 20{x}^{2}$

■ $20{x}^{2} = 28x - 14x$

■ $20{x}^{2} = 14x$

■ $20{x}^{2} - 14x = 0$

■ $2x ( 10x - 7) = 0$

Vamos posar :

$2x = 0\:\:e\:\:10x - 7 = 0$

$x = 0\:\:e\:\:10x = 7$

$x = 0\:\:e\:\:x = \dfrac{7}{10}$

✯$\boxed{\boxed{S = \{0\:;\:\dfrac{7}{10}\}}}$✅

↔ Substitua x por $\dfrac{7}{10}$ para verificar a igualdade. ↔

• $\:\dfrac{14}{\dfrac{7}{10}} = \dfrac{14}{2(\dfrac{7}{10})} + 10$

• $\:\dfrac{14 \times10}{7} = \dfrac{14}{\dfrac{14}{10}} + 10$

• $\:\dfrac{140}{7} = \dfrac{14 \times10}{14} + 10$

• $\:20 = \dfrac{140}{14} + 10$

• $\:20 = 10 + 10$

• $\:20 = 20$

Answer 2

Explicação passo-a-passo:

$\sf \dfrac{14}{x}=\dfrac{14}{2x+10}$

$\sf \dfrac{\not{14}}{x}=\dfrac{\not{14}}{2x+10}$

$\sf \dfrac{1}{x}=\dfrac{1}{2x+10}$

$\sf 2x+10=x$

$\sf 2x-x=-10$

$\sf \red{x=-10}$