= Solution
With the forward direction defined as cis-to-trans, the elementary steps have rates $k_1[\mathrm{cis}]$ and $k_{-1}[\mathrm{trans}]$. One trans molecule is gained per forward event and lost per reverse event, so
$$
\boxed{\frac{\mathrm d[\mathrm{trans}]}{\mathrm dt}=k_1[\mathrm{cis}]-k_{-1}[\mathrm{trans}].}
$$
Each <rate constant> has units $\mathrm{s^{-1}}$, and the right side has units of <concentration> per unit <time>. This net rate can have either sign, even though the individual event rates are nonnegative.
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