Question

if $overline{ux}congoverline{wx}$, $uv = 2s - 3$, and $vw = s$, what is the value of $s$?

Explanation:

Step1: Apply congruent - segment property

Since $\overline{UX}\cong\overline{WX}$, and $X$ is likely on the perpendicular - bisector of $\overline{UW}$ (by the property of congruent segments in a geometric figure), we can assume that $UV = VW$ (by some geometric congruence or symmetry property related to the figure).
$2s - 3=s$

Step2: Solve the equation for $s$

Subtract $s$ from both sides of the equation: $2s - s-3=s - s$.
We get $s - 3 = 0$.
Then add 3 to both sides: $s-3 + 3=0 + 3$.

Answer:

$3$