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

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