[tex]\begin{gathered} (a)\text{ a+b = a}+(-a) \\ \text{ a+b = a-a} \\ \text{ a+b =0} \\ \end{gathered}[/tex]
(b) We know that a and b are both the same distance away from zero. However, we can see from the preceding number line that a and b are on opposite sides of zero.
If we start at zero and move units to the right, and then move the same number of units to the left, we will be back at 0.
This can also be expressed symbolically. We know they are opposites because a and b are the same distance from zero but on opposite sides of zero, therefore b=-a. A number's sum and its inverse are always zero.
