Evaluate 4 - 3 - (-2) - [12 - 3 + 4].

Step-by-step solution

1. 1

   Evaluate the bracket first. Brackets outrank every other operation, and inside them addition and subtraction run left to right:

   $12-3+4=9+4=13.$

   A common slip is to treat $-3+4$ as a unit and compute $12-7=5$; addition and subtraction have equal precedence, so the left-to-right order is what decides.

2. 2

   Rewrite the expression with the bracket replaced. Substituting $13$ and keeping the minus sign that was in front of it:

   $4-3-(-2)-13.$

   The square brackets are only grouping symbols here — they carry no multiplication, so no distribution is involved.

3. 3

   Convert the double negative. Subtracting a negative number is the same as adding its magnitude:

   $-(-2)=+2,$

   so the expression becomes

   $4-3+2-13.$

   Parentheses around $-2$ exist purely to separate the two signs; they do not change the value of the number.

4. 4

   Add and subtract from left to right. One term at a time:

   $4-3=1,\qquad 1+2=3,\qquad 3-13=-10.$

   So the value of the expression is $-10$.

5. 5

   Check by regrouping. Splitting into positives and negatives, $(4+2)-(3+13)=6-16=-10$ ✓. This regrouping is legitimate because every term keeps its own sign, and it gives an independent route to the same answer.