﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.01,0:00:04.45,Default,,0000,0000,0000,,But where does this show up in my equation? If we subtract 4 from both sides, Dialogue: 0,0:00:04.55,0:00:09.10,Default,,0000,0000,0000,,we're going to isolate the absolute value. We'll get the distance of p plus 3 Dialogue: 0,0:00:09.11,0:00:13.58,Default,,0000,0000,0000,,alone. This is where the 8 shows up. The absolute value or the distance of p Dialogue: 0,0:00:13.59,0:00:18.16,Default,,0000,0000,0000,,plus 3 from 0 must be 8. When solving absolute value equations, we need to make Dialogue: 0,0:00:18.17,0:00:22.72,Default,,0000,0000,0000,,sure we get the absolute value symbol on one side of the equation alone. That Dialogue: 0,0:00:22.74,0:00:26.74,Default,,0000,0000,0000,,way, we can represent the distance. Once we isolate the absolute value, we want Dialogue: 0,0:00:26.74,0:00:30.82,Default,,0000,0000,0000,,to check. We want to make sure that it's greater than or equal to 0. Remember, Dialogue: 0,0:00:30.83,0:00:34.95,Default,,0000,0000,0000,,distance is always positive, so if we had a negative answer on this side, there Dialogue: 0,0:00:34.96,0:00:38.99,Default,,0000,0000,0000,,would be any number that could make it true, there'd be no solution. This is a Dialogue: 0,0:00:39.00,0:00:42.71,Default,,0000,0000,0000,,difficult concept and it's one that we'll stumble upon, too, later. Dialogue: 0,0:00:42.72,0:00:47.30,Default,,0000,0000,0000,,So now, we're back into the same case before. The value of p plus 3 could be 8 Dialogue: 0,0:00:47.31,0:00:52.04,Default,,0000,0000,0000,,units to left of 0 at negative 8, or it could be 8 units to the right of 0, at Dialogue: 0,0:00:52.05,0:00:57.10,Default,,0000,0000,0000,,positive 8. So, let's split this equation up into 2 equations, setting p plus 3 Dialogue: 0,0:00:57.12,0:01:01.46,Default,,0000,0000,0000,,to negative 8 and p plus 3 equal to positive 8. Just like from before. And at Dialogue: 0,0:01:01.47,0:01:05.65,Default,,0000,0000,0000,,this point, you might even be able to solve it in your head, which is great. For Dialogue: 0,0:01:05.66,0:01:09.49,Default,,0000,0000,0000,,more complicated questions, it's best to stick to the equation solving. Dialogue: 0,0:01:09.59,0:01:13.63,Default,,0000,0000,0000,,Subtracting 3 from both sides, p could equal 5. And subtracting 3 from both Dialogue: 0,0:01:13.65,0:01:17.91,Default,,0000,0000,0000,,sides, p could equal negative 11. So, the solution set or the values for p, are Dialogue: 0,0:01:17.92,0:01:21.83,Default,,0000,0000,0000,,negative 11 and 5. And just like all our other equations, we can check these Dialogue: 0,0:01:21.85,0:01:25.30,Default,,0000,0000,0000,,values in our original equation to see if we are right. That's one of the Dialogue: 0,0:01:25.31,0:01:29.11,Default,,0000,0000,0000,,beauties of mathematics. This can help build your confidence in math. If this Dialogue: 0,0:01:29.12,0:01:32.94,Default,,0000,0000,0000,,don't check, maybe it's a good idea to look back at your work. You might rethink Dialogue: 0,0:01:32.95,0:01:34.62,Default,,0000,0000,0000,,your process or catch a small error.