Question

resuelve
1) 3 (x+4)-2(x-5)=2(x+11)-x
2) a (x+1)-3a=b-b(x-1)
3) x (2m+n)=n(x+3);m =/ 0
4) $\frac{x}{x - 1} +3 = \frac{x}{x \times 1}$

Answer 1

1)

$3(x + 4) - 2(x - 5) = 2(x + 11) - x \\ 3 \times x + 3 \times 4 - 2 \times x - 2 \times - 5 = 2 \times x + 2 \times 11 - x \\ 3x + 12 - 2x + 10 = 2x + 22 - x \\ x + 22 = x + 22 \\ x - x = 22 - 22 \\ 0 = 0$

X puede tomar cualquier valor

2)

$a(x + 1) - 3a = b - (x - 1) \\ a(x + 1 - 3) = b(1 - x + 1) \\ a(x - 2) = b(2 - x) \\ a(x - 2) = - b(x - 2) \\ a = - b \: \: \: y \: \: \: x≠2$

X toma cualquier valor, menos el 2

3)

$x(2m + n) = n(x + 3) \\ 2xm + xn = xn + 3n \\ 2xm = 3n + xn - xn \\ 2xm = 3n \\ x = \frac{3n}{2m}$

4)

$\frac{x}{x - 1} + 3 = \frac{x}{x \times 1} \\ \frac{x}{x - 1} + \frac{3(x - 1)}{x - 1} = \frac{x}{x} \\ \frac{x + 3x - 6}{x - 1} = 1 \: \: \: \: \: \: \: \: \: \: \: \: \\ 4x - 6 = x - 1 \\ 3x = 5 \\ x = \frac{3}{5}$