Question

Pessoal me ajudem. Resolva a equação

Answer 1

x - 1      x     (2x - 1)
------ = ---- - -------- 
  5         1        3

3x - 3 = 15x - 10x + 5
----------------------------
             15                 → mmc de 3 e 5

5x - 3x = - 5 - 3
2x = - 8
x = -4

Answer 2

Dada a equação:

$\mathsf{\dfrac{x-1}{5}=x-\dfrac{2x-1}{3}}$

Multiplicando ambos os termos por 15 (MMC de 3 e 5):

$\mathsf{15\cdot \dfrac{x-1}{5}=15\cdot \left(x-\dfrac{2x-1}{3}\right)}\\\\\\\mathsf{3\cdot \left(x-1\right)=15\cdot \left(\dfrac{3x}{3}-\dfrac{2x-1}{3}\right)}\\\\\\\mathsf{3x-3=15\cdot \dfrac{3x-\left(2x-1\right)}{3}}\\\\\\\mathsf{3x-3=5\cdot \left(3x-2x+1\right)}\\\\\\\mathsf{3x-3=5\cdot \left(x+1\right)}\\\\\\\mathsf{3x-3=5x+5}\\\\\\\mathsf{5x-3x=-3-5}\\\\\\\mathsf{2x=-8}\\\\\\\mathsf{x=-\dfrac{8}{2}}\\\\\\\boxed{\mathsf{x=-4}}\: \: \checkmark$