1. The problem states: The product of a number and 14, increased by 28 is 98. 2. Let the number be $x$. The product of the number and 14 is $14x$. 3. Increased by 28 means we add 28 to $14x$, so the expression is $14x + 28$. 4. According to the problem, this expression equals 98, so the equation is: $$14x + 28 = 98$$ 5. To solve for $x$, subtract 28 from both sides: $$14x = 98 - 28$$ $$14x = 70$$ 6. Divide both sides by 14: $$x = \frac{70}{14}$$ $$x = 5$$ 7. Therefore, the number is 5.