Answer
$x=7$ and $x=-2$
Work Step by Step
$|2x-5|=9$
By the definition of absolute value, solving this equation is equivalent to solving two separate equations, which are:
$2x-5=9$ and $2x-5=-9$
Solve both equations for $x$:
$2x-5=9$
$2x=9+5$
$2x=14$
$x=\dfrac{14}{2}=7$
$2x-5=-9$
$2x=-9+5$
$2x=-4$
$x=-\dfrac{4}{2}=-2$