To determine $x$ in the given triangle, we will proceed as follows:

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Step 1: Determine angle $\angle ACD$

From the diagram, we know that:
$\angle ACD + \angle DCB = 180^\circ \ \text{(linear pair of angles).}$
Given $\angle DCB = 131^\circ$, we can calculate $\angle ACD$:
$\angle ACD = 180^\circ - 131^\circ = 49^\circ.$

Thus, $\angle ACD = 49^\circ$.

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Step 2: Solve for $x$ using the Law of Sines

In triangle $ABC$, we apply the Law of Sines:
$\frac{AB}{\sin(\angle ACB)} = \frac{AC}{\sin(\angle ABC)}.$

We are given:

• $AB = 3 \ \text{cm}$,
• $\angle ABC = 49^\circ$,
• ( \angle ACD