Question

8) calcule o valor de X em cada uma da proporções:


a) x+6/×-6 = 2/3

b) 1/5 = x-6/x+1,5​

Answer 1

a)

$\frac{x + 6}{x - 6} = \frac{2}{3}$

$3 (x + 6) = 2(x - 6)$

$3x + 18 = 2x - 12$

$3x - 2x = - 12 + 18$

$x = - 30$

b)

$\frac{1}{5} = \frac{x - 6}{x + 1,5}$

$\frac{1}{5} = \frac{x - 6}{x + \frac{15}{10} }$

$\frac{1}{5} = \frac{x - 6}{x + \frac{3}{2} }$

$\frac{1}{5} = \frac{x - 6}{ \frac{x}{1} + \frac{3}{2} }$

$\frac{1}{5} = \frac{x - 6}{ \frac{2x}{2} + \frac{3}{2} }$

$\frac{1}{5} = \frac{x - 6}{ \frac{2x + 3}{2} }$

$\frac{1}{5} = \frac{(x + 6) \times 2}{2x + 3}$

$\frac{1}{5} = \frac{2x - 12}{2x + 3}$

$2x + 3 = 5(2x - 12)$

$2x + 3 = 10x - 60$

$2x - 10x = - 60 - 3$

$- 8x = - 63( . - 1)$

$8x = 63$

$x = \frac{63}{8} = 7.875$