To solve this equation, we need to find the value of x that satisfies the equation.

9 + 2|x| = 12 - |x|

First, we can simplify the equation by isolating the absolute value terms on one side:

2|x| + |x| = 12 - 9

Combining like terms:

3|x| = 3

Now we can solve for |x| by dividing both sides by 3:

|x| = 1

This means that x can be either 1 or -1.