1. **Stating the problem:** We need to find the value of $x$ in an addition problem where the total was mistakenly taken as 540 instead of 431. 2. **Understanding the problem:** If the sum was assumed to be 540 but the correct sum is 431, the difference must be accounted for by $x$. 3. **Setting up the equation:** Let the original sum without $x$ be $S$. Then: $$S + x = 540$$ But the correct total is 431, so: $$S + x = 431$$ 4. **Finding $x$:** Since the sum was mistakenly taken as 540, the difference is: $$540 - 431 = 109$$ 5. **Conclusion:** The value of $x$ that accounts for the difference is: $$x = 109$$ Therefore, $x$ equals 109.