Evaluate -2 x (-4) - (-4) + 3 - (-3) x 5 using the order of operations.

Step-by-step solution

1. 1

   Decide the order before computing anything. There are no brackets to evaluate and no exponents, so the order of operations says: all multiplications first, then the additions and subtractions from left to right. The parentheses here only mark negative numbers — they are not grouping operations to be worked out.

2. 2

   Do the two multiplications. A product of two negatives is positive, and a negative times a positive is negative:

   $-2\times(-4)=+8,\qquad (-3)\times 5=-15.$

   Substituting these back, the expression becomes

   $8-(-4)+3-(-15).$

   Keep the surrounding signs attached when you substitute: the $-15$ replaces $(-3)\times 5$, so the term is $-(-15)$, not $-15$.

3. 3

   Convert every "subtract a negative" into an addition. Subtracting a negative reverses direction twice, so $a-(-b)=a+b$:

   $8-(-4)=8+4,\qquad -(-15)=+15.$

   The expression is now free of double signs:

   $8+4+3+15.$

   This is where most errors happen; writing the double-negative conversion as a separate line makes it much harder to lose a sign.

4. 4

   Add left to right. Accumulating one term at a time:

   $8+4=12,\qquad 12+3=15,\qquad 15+15=30.$

   So the value of the expression is $30$.

5. 5

   Re-check by grouping differently. Addition is associative and commutative, so pairing $(8+15)+(4+3)=23+7=30$ must give the same total — and it does. Because every term ended up positive, the answer had to exceed the largest single term $15$, which is a quick plausibility test.