But where does this show up in my equation? If we subtract 4 from both sides,
we're going to isolate the absolute value. We'll get the distance of p plus 3
alone. This is where the 8 shows up. The absolute value or the distance of p
plus 3 from 0 must be 8. When solving absolute value equations, we need to make
sure we get the absolute value symbol on one side of the equation alone. That
way, we can represent the distance. Once we isolate the absolute value, we want
to check. We want to make sure that it's greater than or equal to 0. Remember,
distance is always positive, so if we had a negative answer on this side, there
would be any number that could make it true, there'd be no solution. This is a
difficult concept and it's one that we'll stumble upon, too, later.
So now, we're back into the same case before. The value of p plus 3 could be 8
units to left of 0 at negative 8, or it could be 8 units to the right of 0, at
positive 8. So, let's split this equation up into 2 equations, setting p plus 3
to negative 8 and p plus 3 equal to positive 8. Just like from before. And at
this point, you might even be able to solve it in your head, which is great. For
more complicated questions, it's best to stick to the equation solving.
Subtracting 3 from both sides, p could equal 5. And subtracting 3 from both
sides, p could equal negative 11. So, the solution set or the values for p, are
negative 11 and 5. And just like all our other equations, we can check these
values in our original equation to see if we are right. That's one of the
beauties of mathematics. This can help build your confidence in math. If this
don't check, maybe it's a good idea to look back at your work. You might rethink
your process or catch a small error.