To solve the equation \((3x - 16) \cdot 49 = 98\), follow these steps:

1. **Divide both sides by 49** to isolate the term involving \(x\):
\[
\frac{(3x - 16) \cdot 49}{49} = \frac{98}{49}
\]
Simplifying this, we get:
\[
3x - 16 = 2
\]

2. **Add 16 to both sides** to isolate the term involving \(x\):
\[
3x - 16 + 16 = 2 + 16
\]
Simplifying this, we get:
\[
3x = 18
\]

3. **Divide both sides by 3** to solve for \(x\):
\[
\frac{3x}{3} = \frac{18}{3}
\]
Simplifying this, we get:
\[
x = 6
\]

So, the solution to the equation \((3x - 16) \cdot 49 = 98\) is \(x = 6\).