Solve the equation a + (-16) = -4.

Step-by-step solution

1. 1

   Rewrite the added negative as a subtraction. For any numbers, $p+(-q)=p-q$, so the double sign collapses:

   $a-16=-4$

   Doing this first removes the visual clutter that causes most sign errors here.

2. 2

   Undo the subtraction. Add $16$ to both sides:

   $a-16+16=-4+16$

3. 3

   Evaluate the right-hand side. Adding a positive to a negative moves right along the number line:

   $a=-4+16=12$

4. 4

   Check and sanity-test the sign. $12+(-16)=12-16=-4$ $\checkmark$. The check also matches intuition: to land on $-4$ after losing $16$, you must have started $16$ above $-4$, and $-4+16=12$.