Answer: $25$

Explanation:1. Understand the problem: A piece of string with a length of $35$ inches is cut into two parts. One part has a length of $x$ inches. The other part has a length of $y$ inches. The value of $x$ is $5$ more than $2$ times the value of $y$. We need to find the value of $x$.

2. Set up a system of equations: Equation 1 (total length): $x + y = 35$ Equation 2 (relationship between x and y): $x = 2y + 5$

3. Solve the system of equations: We can use substitution. Substitute Equation 2 into Equation 1: $(2y + 5) + y = 35$ Combine like terms: $3y + 5 = 35$ Subtract $5$ from both sides: $3y = 35 - 5$ $3y = 30$ Divide by $3$: $y = \dfrac{30}{3}$ $y = 10$

4. Find the value of $x$: Substitute the value of $y$ back into Equation 2: $x = 2y + 5$ $x = 2(10) + 5$ $x = 20 + 5$ $x = 25$

5. Check with Equation 1 (optional): $x+y = 25+10 = 35$. This is correct.

6. Conclusion: The value of $x$ is $25$.