Solve the Double Absolute Value Equation: |-x| = 10

To solve this problem, we'll follow these steps:

• Step 1: Use the definition of absolute value to create equations.
• Step 2: Solve each equation to find possible values of $x$.
• Step 3: Check the solutions against the original problem.

Now, let's work through each step:
Step 1: The equation is given as $\left| -x \right| = 10$. According to the definition of absolute value:

• Case 1: $-x = 10$
• Case 2: $-x = -10$

Step 2: Solve each case:
In Case 1, we have:

• $-x = 10$
  This implies $x = -10$.

In Case 2, we have:

• $-x = -10$
  This implies $x = 10$.

Step 3: Therefore, the possible solutions are $x = -10$ and $x = 10$, which satisfy the equation independently.

The solution to the problem is:

$x = -10$ , $x = 10$