1. The problem is to solve the equation $7 - (-x) = 12$ for $x$. 2. Recall that subtracting a negative number is the same as adding its positive counterpart. So, $7 - (-x)$ becomes $7 + x$. 3. Rewrite the equation: $$7 + x = 12$$ 4. To isolate $x$, subtract 7 from both sides: $$7 + x - \cancel{7} = 12 - \cancel{7}$$ $$x = 5$$ 5. The solution is $x = 5$. 6. The number line graph shows points at $-5$ and $1$ with an arc labeled 6, which is unrelated to the solution of this equation. 7. The key step is understanding that subtracting a negative is addition, which simplifies the equation to a basic linear form.