Question

(x-4)/5=9-(2x-41)/9

Answer 1

For this question, you have to take Least Common Multiplier for which in this case will be "45" as, the denominators can get similar and get multiplied by a same value to form a similar expression. This allows us to cancel out them by common factors. Full process shown below.

$\mathbf{Given \: \: Expression: \: \dfrac{x - 4}{5} = 9 - \dfrac{2x - 41}{9}}$

$\mathbf{\dfrac{x - 4}{5} \times 45 = 9 \times 45 - \dfrac{2x - 41}{9} \times 45}$

$\mathbf{9(x - 4) = 405 - 5 (2x - 41)}$

$\mathbf{9x - 36 = 405 - 10x + 205}$

$\mathbf{9x - 36 = - 10x + 610}$

$\mathbf{9x - 36 + 36 = - 10x + 610 + 36}$

$\mathbf{9x = - 10x + 646}$

$\mathbf{9x + 10x = - 10x + 646 + 10x}$

$\mathbf{19x = 646}$

$\mathbf{\dfrac{19x}{19} = \dfrac{646}{19}}$

$\mathbf{\therefore \quad x = 34}$

$\boxed{\mathbf{\underline{\therefore \quad Final \: \: Answer \: \: is; \: \: x = 34}}}$

Hope it helps.