8 - (-3) = 11 There are 2 steps to solving this problem
1. We change the subtraction problem to an addition problem.
1st 8 - (-3) = 11 becomes 8 + (-3) = 11
2. Then we change the sign of the number that immediately follows the subtraction sign and treat the problem like an addition problem
2nd 8 + (+3) = 11
Think about this. If all you have is $12 but owe someone $3, then you are worth $9. (Debts are written as negative numbers.) So
$12 + (-$3 debt) = $9
But someone pays your $3 debt. Someone has taken away a $3 debt and hence you are worth $3 more. Mathematically we can write this :
$12 + (-$3 debt) - (-$3 debt) = $12 +(-3) + (+$3 debt) = $12
In effect they are adding $3 to your wealth by subtracting a $3 debt. So the problem changes
by subtracting a debt. Remember that mathematics is a system and the only way the system can work in the above problem is if we change the subtraction to addition so the problem $12 + (-$3) - (-$3) ends up $12 + ($-3) + (+$3) = $12