Question

Calcule o valor de x nas seguintes proporçoes.

Answer 1

Explicação passo-a-passo:

a)

$\sf \dfrac{6}{8}=\dfrac{9}{x}$

$\sf 6x=8\cdot9$

$\sf 6x=72$

$\sf x=\dfrac{72}{6}$

$\sf \red{x=12}$

b)

$\sf \dfrac{2x}{5}=\dfrac{8}{10}$

$\sf 2x\cdot10=5\cdot8$

$\sf 20x=40$

$\sf x=\dfrac{40}{20}$

$\sf \red{x=2}$

c)

$\sf \dfrac{x}{3x-2}=\dfrac{6}{3}$

$\sf 6\cdot(3x-2)=3x$

$\sf 18x-12=3x$

$\sf 18x-3x=12$

$\sf 15x=12$

$\sf x=\dfrac{12}{15}$

$\sf \red{x=\dfrac{4}{5}}$

d)

$\sf \dfrac{\frac{2}{5}}{\frac{4}{3}}=\dfrac{\frac{3}{5}}{x}$

$\sf \dfrac{2x}{5}=\dfrac{4}{\not{3}}\cdot\dfrac{\not{3}}{5}$

$\sf \dfrac{2x}{\not{5}}=\dfrac{4}{\not{5}}$

$\sf 2x=4$

$\sf x=\dfrac{4}{2}$

$\sf \red{x=2}$

e)

$\sf \dfrac{x-5}{3}=\dfrac{x-1}{5}$

$\sf 5\cdot(x-5)=3\cdot(x-1)$

$\sf 5x-25=3x-3$

$\sf 5x-3x=-3+25$

$\sf 2x=22$

$\sf x=\dfrac{22}{2}$

$\sf \red{x=11}$

f)

$\sf \dfrac{\frac{x-2}{3}}{\frac{x-1}{2}}=\dfrac{1}{2}$

$\sf 2\cdot\Big(\dfrac{x-2}{3}\Big)=1\cdot\Big(\dfrac{x-1}{2}\Big)$

$\sf \dfrac{2x-4}{3}=\dfrac{x-1}{2}$

$\sf 2\cdot(2x-4)=3\cdot(x-1)$

$\sf 4x-8=3x-3$

$\sf 4x-3x=-3+8$

$\sf \red{x=5}$