Answer
$$x = -7$$
Work Step by Step
We have $$\frac{x-3}{5} - 1 = \frac{x- 5}{4}$$
As we see we have rational terms in both of the sides of the equation so we are going to multiply each side of the equation with the minimum common multiple of the denominators to maintain the equality. The mcm of $5$ and $4$ is $20$ $$20*(\frac{x-3}{5} - 1) = 20*(\frac{x- 5}{4})$$ $$\frac{20*(x-3)}{5} + 20*(-1) = \frac{20*(x- 5)}{4}$$
Simplifying each fraction $$4*(x-3) + 20*(-1) = 5*(x- 5)$$
Doing the multiplications in order to eliminate the parenthesis and taking in count the sings law $$4*x + 4*(-3) + 20*(-1) = 5*x + 5*(-5)$$ $$4x -12 - 20 = 5x - 25$$
Taking $x$ terms to the left side of the equation and numbers to the right $$4x - 5x = -25 + 20 + 12$$
Simplifying $$-x = 7$$
Multiplying each side of the equation by $-1$ $$x = -7$$
