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Solution:
Given parallelogram LOMN, and the diagonals OM and LN
We know a property that the diagonals of parallelogram bisect each other, hence they divide into two equal halves
So, OQ = QM
2x + 3 = 3x - 4
3 + 4 = 3x - 2x
7 = x
Hence, OM = OQ + QM
OM = 2x + 3 + 3x - 4
OM = 5x - 1
OM = 5(7) - 1
OM = 35 - 1
OM = 34
Therefore, OM = 34
Summary:
In parallelogram LONM, the value of OM is 34.