 In this video, I'm going to do a couple of extra examples for solving linear equations using distributive property. So notice what I have up here, I have two of the same equations. I'm going to very quickly go through and show you two different ways of solving these equations. I'm going to do this a lot quicker than I did in a previous video where I explained why we use distributive property and my first video on these. Anyway, so first of all I'm going to use distributive property to solve this. So this four that's out front, I'm going to distribute it to everything inside. So I'm going to take 4 times x, which is 4x, 4 times negative 3, which is negative 12, and 4, nope, oh, that's it. Only inside the parentheses. Don't take that 4 times 48, I almost made that mistake. So equals 48, that guy just comes down, and again, the entire goal behind solving equations is to get the variable by itself. So this x I need to get by itself. So get rid of this negative 12, get rid of the 4, so I'm going to add 12 to both sides, add 12 to both sides. Okay, and then after that I'm going to divide by 4. x is then equal to, 4 goes into 6 once, remainder 20, 4 goes into 25 times. So x is equal to 15. Does that work? You can always take 15, plug it back up, 15 minus 3 is 12, 12 times 4 is 48. So yes, it does work. So that's one great thing about linear equations. You can always take your answers, plug them back into your original equation and see if they do work. Yes, it does. Okay, and now for this other one, I'm not going to use distributive property, I'm going to use it as kind of a different method. So instead of taking the 4 and distributing it, I'm going to take the 4, since it's multiplying here times x, I'm going to divide by 4 instead. So 4 divided by 4, those cancel, I'm just left with x minus 3 equals, 4 goes to 48, 1, 12 times. That was actually pretty simple. That might be an easier way of solving, because the only thing I have to do is get rid of this negative 3, so I have to add 3 to both sides. So x in this case is equal to 15. This actually is a pretty good example, because this shows you the difference between the two methods. This distributive property method is actually longer, it takes you longer to figure out what the answer is, as opposed to doing it this way, as opposed to just cancelling the 4 off right away, that's actually pretty short. It just kind of depends, that's not always going to happen, it just kind of depends on the problem. Okay, so there's one example, let me do one more, and again this other example, this next one I will do twice, once with distributive property and once without. This one's kind of similar, 4 times m plus 12 equals negative 36, m plus 12 equals negative 36. Alright, so again I'm going to go through this kind of quickly. So the first thing I'm going to do is I'm going to distribute this 4 times everything inside. So 4 times m is 4m, 4 times 12 is 48 equals negative 36, okay. So to solve for m, I got to subtract 48 from both sides, subtract 48, okay now I always write these down because now I have a negative 36 and a negative 48, since those are both negative numbers, I actually add those together to get 70, 80, 84, negative 84, 4m, and this right here goes to zero, so all I'm left with is 4m, and then these two actually add together to get a larger negative number, negative 84, and then from there I'm going to divide by 4, divide by 4, those cancel ones, m equals, 4 goes into 8 twice, 4 goes into 4 once, 1 negative, so I'll have a negative 21, okay let's see if I did that right, take negative 21 and plug it back up in here, negative 21 plus 12 that would be negative 9, negative 9 times 4 is a negative 36, so that does work, okay. So that was using distributive property, now I'm not going to use distributive property, so the first thing that I would do is to get rid of this 4, so I'm going to divide by 4, those cancel, I'm left with just what's inside the parentheses, m plus 12 equals, I'm going to divide here, 4 goes into 36, negative 9 times, alright now as you can probably see this is going to be a shorter method of solving because now the only thing I have to get rid of is this 12, so I just subtract 12 from both sides, m is then equal to negative 9 and negative 12 that makes a negative 21, negative 21 here, negative 21 there, doing this twice reassures me that yes I did do this correctly, also if I take negative 21, plug it back up into the original equation that also tells me I did it correctly, okay there's just a few more examples of solving linear equations using the distributive property, so you can either use the distributive property to solve this or well actually you don't have to use distributive property, you can instead get rid of the number out front first and then solve, sometimes it will be faster, sometimes it will be slower, just kind of depends on the problem.