Answer
x = -7
Work Step by Step
$\frac{x-3}{5}$ - $1$= $\frac{x-5}{4}$
Find the least common multiple:
5 : $5$
4 : $2\times2$
Hence, the LCM is $5\times2\times2 = 20$
Multiply the whole equation by the LCM:
$[\frac{x-3}{5} - 1]\times20$ = $[\frac{x-5}{4}]\times20$
$4(x-3) - 20$ = $5(x-5)$
Expand $4(x-3)$ = $4x - 12$
Expand $5(x-5)$ = $5x-25$
Rewrite the equation:
$4x - 12 -20$ = $5x-25$
$4x -32$ = $5x-25$
Add 32 to both sides:
$4x -32 + 32$ = $5x-25 + 32$
$4x$ = $5x+7$
Simplify:
$x=-7$
