Question

resolva as equações no conjunto universo dos números racionais letra a) x/2 + x/4 = x+6/2, letra b) x-3/2 +3x= 5x+27/2, letra c) 2x+8/2 + x+ 2/4 =-8, letra d) x-1/5 =x - 2x-6/5
rápido gente por favor!!!​

Answer 1

Resposta:

$a) \: \frac{x}{2} + \frac{x}{4} = \frac{x + 6}{2} \\ \\ \frac{2x + x = 2 \times (x + 6)}{4} \\ \\ 2x + x = 2 \times (x + 6) \\ 3x = 2x + 12 \\ 3x - 2x = 12 \\ x = 12$

$b) \: \frac{x - 3}{2} + 3x = \frac{5x + 27}{2} \\ \\ \frac{x - 3 + 6x = 5x + 27}{2} \\ \\ x - 3 + 6x = 5x + 27 \\ 7x - 3 - 5x - 27 = 0 \\ 2x - 30 = 0 \\ 2x = 30 \\ \\ x = \frac{30}{2} \\ \\ x = 15$

$c) \: \frac{2x + 8}{2} + \frac{x + 2}{4} = - 8 \\ \\ \frac{2 \times (2x + 8) + x + 2 = - 32}{4} \\ \\ 2 \times (2x + 8) + x + 2 = - 32 \\ 4x + 16 + x + 2 = - 32 \\ 5x + 18 = - 32 \\ 5x = - 32 - 18 \\ 5x = - 50 \\ \\ x = - \frac{50}{5} \\ \\ x = - 10$

$d) \: \frac{x - 1}{5} = x - \frac{2x - 6}{5} \\ \\ \frac{x - 1 = 5x - (2x - 6)}{5} \\ \\ x - 1 = 5x -( 2x - 6) \\ x - 1 = 5x - 2x + 6 \\ x - 1 = 3x + 6 \\ x - 1 - 3x - 6 = 0 \\ - 2x - 7 = 0 \\ - 2x = 7 \\ \\ x = - \frac{ 7}{2}$