Answer
$x = 4$
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 $\overline{BD}$ is the perpendicular bisector of $\overline{AC}$; therefore, $B$ is equidistant from $A$ and $C$. $AB$, thus, is equal to $BC$.
We set thes
e two line segments equal to one another to find $x$:
$AB = BC$
$2x - 1 = 7$
$2x = 8$
$x = 4$
