Answer
The solutions are $x=\dfrac{7}{2}$ and $x=\dfrac{5}{2}$
Work Step by Step
$\Big|\dfrac{5}{x-3}\Big|=10$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$\dfrac{5}{x-3}=10$ and $\dfrac{5}{x-3}=-10$
Solve the first equation:
$\dfrac{5}{x-3}=10$
Take $x-3$ to multiply the right side:
$5=10(x-3)$
$5=10x-30$
Solve for $x$:
$-10x=-5-30$
$-10x=-35$
$x=\dfrac{-35}{-10}$
$x=\dfrac{7}{2}$
Solve the second equation:
$\dfrac{5}{x-3}=-10$
Take $x-3$ to multiply the right side:
$5=-10(x-3)$
$5=-10x+30$
Solve for $x$:
$10x=30-5$
$10x=25$
$x=\dfrac{25}{10}$
$x=\dfrac{5}{2}$
The solutions are $x=\dfrac{7}{2}$ and $x=\dfrac{5}{2}$
