Question

Calcule o valor de X nas proporções:
Alguém me ajuda pfv?

Answer 1

Resposta:

$a) \: \frac{x - 2}{12} = \frac{x}{20} \\ 20 \times (x - 2) = 12x \\ 20x - 40 = 12x \\ 20x - 40 - 12x = 0 \\ 8x - 40 = 0 \\ 8x = 40 \div (8) \\ x = 5$

$b) \: \frac{x + 1}{5} = \frac{x}{3} \\ \\3 \times (x + 1) = 5x \\ 3x + 3 = 5x \\ 3x + 3 - 5x = 0 \\ - 2x + 3 = 0 \\ - 2x = - 3 \times ( - 1) \\ 2x = 3\\\\ x = \frac{3}{2}$

$c) \: \frac{x}{6} = \frac{x + 2}{10} \\ \\10x = 6 \times (x + 2) \\ 10x = 6x + 12 \\ 10x - 6x - 12 = 0 \\ 4x - 12 = 0 \\ 4x = 12 \div (4) \\ x = 3$

$d) \: \frac{x - 1}{7} = \frac{16}{28} \\ 28 \times (x - 1) = 112 \\ 28x - 28 = 112 \\ 28x - 28 - 112 = 0 \\ 28x - 140 = 0 \\ 28x = 140 \div (28) \\ x = 5$

$e) \: \frac{x + 3}{x - 2} = \frac{3}{2} \\ 2 \times (x + 3) = 3 \times (x - 2) \\ 2x + 6 = 3x - 6 \\ 2x + 6 - 3x + 6 = 0 \\ - x + 12 = 0 \\ - x = - 12 \times ( - 1) \\ x = 12$

$f) \: \frac{2}{1} = \frac{15 - x}{x} \\ 2x = 1 \times (15 - x) \\ 2x = 15 - x \\ 2x - 15 + x = 0 \\ 3x - 15 = 0 \\ 3x = 15 \div (3) \\ x = 5$

$g) \: \frac{20}{x + 1} = \frac{16}{x} \\ 20x = 16 \times (x + 1) \\ 20x = 16x + 16 \\ 20x - 16x - 16 = 0 \\ 4x - 16 = 0 \\ 4x = 16 \div (4) \\ x = 4$

$h) \: \frac{3}{2} = \frac{x + 3}{x - 1} \\ \\ 3 \times (x - 1) = 2 \times (x + 3) \\ 3x - 3 = 2x + 6 \\ 3x - 3 - 2x - 6 = 0 \\ x - 9 = 0 \\ x = 9$