Simplify each of these: 5 - 7, -3 - (-3), 3 + (-2), 9 - (-1), -4 - (-8), and -2 - 3.

Step-by-step solution

1. 1

   Rewrite every subtraction as an addition first. The single rule $a-b=a+(-b)$ removes all the ambiguity about stacked signs, and it converts the two hardest patterns into easy ones: subtracting a negative becomes adding a positive.

2. 2

   Do the two that move left along the number line. Starting at a number and adding a negative moves left:

   $5-7=5+(-7)=-2,\qquad 3+(-2)=1.$

   For $5+(-7)$, the negative has the larger size, so the answer is negative: $7-5=2$ with a minus sign.

3. 3

   Do the ones where a negative is subtracted. Each becomes an addition of a positive, moving right:

   $-3-(-3)=-3+3=0,\qquad 9-(-1)=9+1=10,\qquad -4-(-8)=-4+8=4.$

   The middle one is worth pausing on: $9-(-1)$ is $10$, not $8$. Subtracting a debt makes you richer.

4. 4

   Do the last one, where both signs point the same way.

   $-2-3=-2+(-3)=-5.$

   Here no sign flips — the $3$ was already positive, so its opposite is $-3$ and the two negatives combine in size.

5. 5

   Collect the six answers and check the pattern.

   $5-7=-2,\quad -3-(-3)=0,\quad 3+(-2)=1,$
   $9-(-1)=10,\quad -4-(-8)=4,\quad -2-3=-5.$

   Every expression whose second sign pair was $--$ came out larger than the first number, and every one with $+-$ or a plain subtraction came out smaller. That is the whole content of the rule.