Answer
$JM = 9$
Work Step by Step
According to the perpendicular bisector theorem, points lying on the perpendicular bisector of a segment are equidistant from the segment's endpoints.
In the diagram, we see that $\overline{MB}$ is the perpendicular bisector of $\overline{JK}$; therefore, $M$ is equidistant from $J$ and $K$. $JM$, thus, is equal to $KM$.
We set these two line segments equal to one another to find $x$:
$JM = KM$
Let's plug in what we know:
$9x - 18 = 3x$
Add $18$ to both sides of the equation to isolate constants on the right side of the equation:
$9x = 3x + 18$
Subtract $3x$ from each side of the equation to isolate the variable on the left side of the equation:
$6x = 18$
Divide each side by $6$ to solve for $x$:
$x = 3$
Now that we have the value of $x$, we can plug it into the expression to find $JM$:
$JM = 9x - 18$
Plug in $3$ for $x$:
$JM = 9(3) - 18$
Multiply first, according to order of operations:
$JM = 27 - 18$
Subtract to find $JM$:
$JM = 9$
