Question

Encuentre el valor de x en las proporciones siguientes:
a) (x + 3) : (x 2) = 3 : 2

b) (x + 1) : 4 = (x + 6) : 2x

c) (x + 4) : 1 = (2 x) : 2

d) (2x + 1): (x+ 1) = 5x : (x + 4)

Answer 1

a)
$(x + 3) \div (x \times 2) = 3 \div 2 \\ (x + 3) \times 2 = 3 \times (x \times 2) \\ 2x + 6 = 3 \times (2x)$
$2x + 6 = 6x \\ 2x - 6x = - 6 \\ - 4x = - 6 \\ x = \frac{3}{2}$
b)
$(x + 1) \div 4 = (x + 6) \div 2x \\ \frac{x + 1}{4} = \frac{x + 6}{2} x \\ \frac{x + 1}{4} = \frac{x(x + 6)}{2}$
$\frac{x + 1}{4} = \frac{ {x}^{2} + 6x}{2} \\ 2(x + 1) = 4( {x}^{2} + 6x) \\ x + 1 - 2 {x}^{2} - 12x$
$- 11x + 1 - 2 {x}^{2} = 0 \\ - 2 {x}^{2} - 11x + 1 = 0 \\ - 1x( - 2) {x}^{2} - 1 \times (11)x - 1 \times 1 = - 1 \times 0$
$2 {x}^{2} + 11x + 1 = 0 \\ \frac{ - 11 + - \sqrt{ {11}^{2} - 4 \times 2 \times ( - 1)} }{2 \times 2}$
Y resolviendo eso te da dos resultados 5,589 y 0,089