To solve this equation, we first need to isolate the variable.

|-х| + 2 = 7

Subtract 2 from both sides:

|-х| = 5

Now, we need to consider two cases, one where x is positive and one where x is negative.

Case 1: x is positive
In this case, the equation becomes:
-x + 2 = 7
-x = 5
x = -5 (but x is positive in this case, so this solution is not valid)

Case 2: x is negative
In this case, the equation becomes:
x + 2 = 7
x = 5 (but x is negative in this case, so this solution is not valid)

Therefore, there are no solutions to this equation.