Question

resolva as equações considerando a propriedade da proporção​

Answer 1

Resposta:

$a) \: \frac{x - 1}{3} = \frac{16}{24} \\ \\ 24 \times(x - 1) = 48 \\ 24x - 24 = 48 \\ 24x - 24 - 48 = 0 \\ 24x - 72 = 0 \\ 24x = 72 \div (24) \\ x = 3$

$b) \: \frac{2}{x + 2} = \frac{4}{2 - x} \\ \\ 2 \times (2 - x) = 4 \times (x + 2) \\ 4 - 2x = 4x + 8 \\ 4 - 2x - 4x - 8 = 0 \\ - 6x - 4 = 0 \\ - 6x = 4 \times ( - 1) \\ 6x = - 4 \\ \\ x = - \frac{4}{6} \div (2) \\ \\ x = - \frac{2}{3}$

$c) \: \frac{x - 1}{x + 1} = \frac{2}{6} \\ \\ 6 \times (x - 1) = 2 \times (x + 1) \\ 6x - 6 = 2x + 2 \\ 6x - 6 - 2x - 2 = 0 \\ 4x - 8 = 0 \\ 4x = 8 \div (4) \\ x = 2$

$d) \: \frac{2x + 1}{2x - 1} = \frac{10}{9} \\ \\ 9 \times (2x + 1) = 10 \times (2x - 1) \\ 18x + 9 = 20x - 10 \\ 18x + 9 - 20x + 10 = 0 \\ - 2x + 19 = 0 \\ - 2x = 19 \times ( - 1) \\ 2x = 19 \\ \\ x = \frac{19}{2}$