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