It is not sufficient to maintain an equilibrium that forces balance in each direction. There must also be no turning force about any point. The following diagram shows a non - uniform rod of weight 100 N held horizontal by tensions
and
in cables attached to either end of the rod.

The centre of gravity of the rod is a distance x froim end A.
Resolving vertically gives
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Subtracting these, and using that
gives
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Then
Taking moments about A gives