Converting a minimum constraint into an equality constraint?

Hi

I have an optimization problem (in a vector x) which is linear except
for one constraint of the form:
c = min{x(1), x(1)/5} where x(1) can be positive or negative.

I can write two constraints of the form c <= x(1) and c <= x(1)/5.
However, this just ensures that c is smaller than the minimum of the
two, but not necessarily equal to the minimum. The cost depends
linearly on c, but I can't replace it with max(c).

Since I would like to use a linear solver (if at all possible), is
there any way I can force c to be equal to the minimum of x(1) and
x(1)/5 using additional linear constraints?

Thanks
Srikanth
.

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