Solving the Equation: x-10 When Absolute Value Equals Zero

To solve the problem $\left|x-10\right|=0$, we use this logical reasoning:

• Step 1: Recognize that the absolute value expression equals zero.
  The property of absolute values states that for $\left|A\right|=0$, $A$ must equal zero.
• Step 2: Apply this principle to the given equation.
  Given $\left|x-10\right|=0$, it follows that $x-10=0$.
• Step 3: Solve for $x$.
  Rearrange the equation $x - 10 = 0$ to find $x = 10$.

The solution to the equation $\left|x-10\right|=0$ is therefore $x = 10$.