Question

DETERMINE O X EM CADA SITUAÇÃO:

a) 7/3 = x/12
b) 2x/15 = 6/9
c) √5/2 = x/√20
d) x+1/5 = x/3
e) 2x-3/2 = x+1/6
f) x/x-2 = x-3/x
g) x-2/x-4 = x+3/x-5

Answer 1

A) $\frac{7}{3} = \frac{x}{12}$
$3x = 84 x = 84/3 x = 28$

B) $\frac{2x}{15} = \frac{6}{9}$
$18x = 90 x = 90/18 x = 5$

C) $\frac{ \sqrt{5} }{2} = \frac{x}{ \sqrt{20} }$
$\sqrt{100} = 2x 10 = 2x x = 2/10 x = 5$

D) $\frac{x+1}{5} = \frac{x}{3}$
$3x+3 = 5x 3x-5x = -3 2x = 3 x = -3/-2 = 1,5$

E)$\frac{2x-3}{2} = \frac{x+1}{6}$
$12x-18 = 2x+2 12x-2x = 18+2 10x = 20 x = 20/10 x = 2$

F) $\frac{x}{x-2} = \frac{x-3}{x}$
$x^{2} = x^{2} -3x-2x+6 x^{2} - x^{2} +3x+2x-6 = 0 3x+2x = 6 x = 6/5$

G) $\frac{x-2}{x-4} = \frac{x+3}{x-5}$
$x^{2} -5x-2x+10 = x^{2} +3x-4x-12 x^{2} -7x+10 = x^{2} -x-12 x^{2} - x^{2} -7x+x = -12-10 -6x = -22$
$x = \frac{22}{6} = \frac{11}{3}$