Solve the Absolute Value Equation: |x+2| = |x-2|

To solve the equation $|x+2|=|x-2|$, we begin by considering the properties of absolute values.

The statement $|A| = |B|$ implies two cases:

• Case 1: $A = B$
• Case 2: $A = -B$

For our problem, consider:

• Case 1: $x + 2 = x - 2$
• Case 2: $x + 2 = -(x - 2)$

Let's solve each case:

• Case 1: $x + 2 = x - 2$
  Subtract $x$ from both sides: $x + 2 - x = x - 2 - x$ Reduce to: $2 = -2$ Since $2 \neq -2$, this case has no solution.
• Case 2: $x + 2 = -(x - 2)$
  Expand the right-hand side: $x + 2 = -x + 2$ Add $x$ to both sides: $x + x + 2 = 2$ This simplifies to: $2x + 2 = 2$ Subtract 2 from both sides: $2x = 0$ Solve for $x$: $x = 0$

Thus, the solution to $|x+2|=|x-2|$ is $x = 0$. The correct answer is the choice: $x = 0$.