Explanation:
RU is a median.
so, U is right in the middle between S and T.
and therefore, SU = UT.
3x + 5 = 5x - 7
12 = 2x
x = 6
so, SU = UT = 3×6 + 5 = 18 + 5 = 23 in.
therefore, ST = 2×23 = 46 in.
furthermore, the centroid splits every median with the ratio 2/1.
so, RQ = 2×QU.
RQ = 5 IN, therefore QU = RQ/2 = 5/2 = 2.5 in.
and RU is then 5 + 2.5 = 7.5 in.
for QV we need to go the other way around.
we know SV = 12 in.
and Q splits it also in the ratio 2/1.
that means we deal with 2+1=3 parts of the median.
SQ gets 2 of these parts, and QV gets 1 of these parts.
12/3 = 4 in power unit.
so,
SQ = 2×4 = 8 in.
QV = 1×4 = 4 in.
I believe your teacher made a mistake with the SU and UT definitions.
because ST is almost 4 times the length of the median SV.
and RU is even shorter than SV.
so, as SU = 23 in, V must be far left of U. and R must be left of U but right of V !
this is an impossible triangle.