Question

calcule o valor de X nas proporções
a)
$\frac{x - 2}{12} = \frac{x}{20}$
b)
$\frac{x + 1}{5} = \frac{x}{3}$
c)
$\frac{x + 3}{x - 2} = \frac{3}{2}$
d)
$\frac{2}{1} = \frac{15 - x}{x}$
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Answer 1

Explicação passo-a-passo:

$\frac{x - 2}{12} = \frac{x}{20} \\ 20 \times (x - 2) = 12 \times x \\ 20x - 40 = 12x \\ 20x - 12x = 40 \\ 8x = 40 \\ x = \frac{40}{8} \\ x = 5$

b)

$\frac{x + 1}{5} = \frac{x}{3} \\ 3 \times (x + 1) = 5 \times x \\ 3x + 3 = 5x \\ 3x - 5x = - 3 \\ - 2x = - 3 \: \times ( - 1) \\ 2x = 3 \\ x = \frac{3}{2}$

c)

$\frac{x + 3}{x - 2} = \frac{3}{2} \\ 2 \times (x + 3) = 3 \times (x - 2) \\ 2x + 6 = 3x - 6 \\ 2x - 3x = - 6 - 6 \\ - x = - 12 \: \times ( - 1) \\ x = 12$

d)

$\frac{2}{1} = \frac{15 - x}{x} \\ 2x = 15 - x \\ 2x + x = 15 \\ 3x = 15 \\ x = \frac{15}{3} \\ x = 5$