Question

Determine o valor de X nas proporções.

a)
$\frac{x}{5} = \frac{21}{35}$
b)
$\frac{3}{4} \div \frac{1}{5} = \frac{90}{x}$
c)
$\frac{9}{13} = \frac{x}{26}$
d)
$\frac{1}{7} = \frac{x - 6}{49}$
e)
$\frac{2x + 1}{10} = \frac{ - 21}{30}$
f)
$\frac{3x + 2}{x + 3} = \frac{ - 40}{25}$
g)
$\frac{0.3}{x} = \frac{ - 6}{9}$
h)
$\frac{0.2}{5} = \frac{x}{200}$

​

Answer 1

Resposta:

$a) \: \frac{x}{5} = \frac{21}{35} \\ \\ 35x = 105 \div (35) \\ x = 3$

$b) \: \frac{3}{4} \div \frac{1}{5} = \frac{90}{x} \\ \\ \frac{3}{4} \times 5 = \frac{90}{x} \\ \\ \frac{15}{4} = \frac{90}{x} \\ \\ 15x = 360 \div (15) \\ x = 24$

$c) \: \frac{9}{13} = \frac{x}{26} \\ \\ 13x = 234 \div (13) \\ x = 18$

$d) \: \frac{1}{7} = \frac{x - 6}{49} \\ \\ 7 \times (x - 6) = 49 \\ 7x - 42 = 49 \\ 7x = 49 + 42 \\ 7x = 91 \div (7) \\ x = 13$

$e) \: \frac{2x + 1}{10} = \frac{ - 21}{10} \\ \\ 10 \times (2x + 1) = - 210 \\ 20x + 10 = - 210 \\ 20x = - 210 - 10 \\ 20x = - 220 \div (20) \\ x = - 11$

$f) \: \frac{3x + 2}{x + 3} = \frac{ - 40}{25} \\ \\ 25 \times (3x + 2) = - 40 \times (x + 3) \\ 75x + 50 = - 40x - 120 \\ 75x + 50 + 40x + 120 = 0 \\ 115x + 170 = 0 \\ 115x = - 170 \div (5) \\ 23x = - 34 \\ \\ x = - \frac{34}{23}$

$g) \: \frac{0.3}{x} = \frac{ - 6}{9} \\ \\ \frac{ \frac{3}{10} }{x} = \frac{ - 6}{9} \\ \\ \frac{3}{10x} = \frac{ - 6}{9} \\ \\ - 60x = 27 \div ( - 60) \\ x = - 27 \div 60 \\ \\ x = - \frac{27}{60}$

*Cancelamos o fator comum 3*

$x = - \frac{9}{20}$

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$h) \: \frac{0.2}{5} = \frac{x}{200} \\ \\ 5x = 40 \div (5) \\ x = 8$