1. The problem is to solve the equation $7 - (-x) = 12$ for $x$. 2. Recall the rule that subtracting a negative number is the same as adding its positive counterpart: $a - (-b) = a + b$. 3. Apply this rule to the equation: $$7 - (-x) = 7 + x$$ 4. So the equation becomes: $$7 + x = 12$$ 5. To isolate $x$, subtract 7 from both sides: $$7 + x - \cancel{7} = 12 - \cancel{7}$$ $$x = 5$$ 6. The solution is $x = 5$. This means that when $x$ is 5, the original equation holds true.