 Now obviously whenever you're solving for this type of equation, you're not going to erase everything, you're checked Everything else is going to follow whatever you did previously, right? So what you're going to do, again, is going to say solve and check, right? Now we've already solved it and we've got the solution of x is equal to 0 and x is equal to 3 If we didn't write our restrictions and eliminate this, because of our restrictions, because we need this The problem with 0 will come up when we're doing a check So solving part of straightforward, we've already figured it out, it was x equals 0 and x equals 3 Let's do a check on this The way you do a check is you just write that one, right? Now when you're doing a check, you don't use the equals sign What you're trying to do is see if when you plug in these numbers into the left side of the equation and into the right side of the equation, if the answers are going to work out If one side is going to equal the other side So you can't put an equal sign and just follow it through and move things around from one side of the equation to the other Whenever you're doing a check, you deal with the left side of the equation, you deal with the right side of the equation Nothing moves over, you can't move it over Because what you're trying to do is check to see if your solutions work in the equation Basically, if your solutions that you've got make this side of the equation equal to that side of the equation So let's do this Let's do x is equal to check on x is equal to 3 first So we're going to do x is equal to 3, we're going to check it And over here we're going to go the left side of the equation That means Lx, in short you just put down Lx So left side of the equation Over here is the right side of the equation What you're going to do is plug in x is equal to 3 into the left side So this is 5 over 3 times 3 Because we're subbing in x is equal to 3 On this side we're going to go 3 times 3 plus 1 over 6 times 3 So wherever you see x, you're plugging in 3 5 over 3 times 3, that's just 5 over 9 Now we can't simplify that anymore So that's just 5 over 9 on this side Over here we've got 3 times 3 is 9 3 times 3 is plus 1 is 10 6 times 3 is 18 Now 5 over 9 is that equal to 10 over 18? Well, yeah it is If you remember, well obviously you should remember If you've come this far, we shouldn't have to go through and simplify this But 2 goes both into 10 and 18 So 10 over 18 is 5 over 9 And the left side of the equation is 5 over 9 The right side of the equation is 5 over 9 And this works out So x is equal to 3 is a solution So you put a little check mark here, so that works You've done your check Now what you have to do is do a check for your other solution x is equal to 0 So let's play it in and go through the work 5 over 3 times 0 So it's the same thing, right? You're just plugging in x is equal to 0 for wherever you see x 3 times 0 plus 1 over 6 times 0 Now this is going to be 5 over 0 This is going to be 3 times 0 is 0 plus 1 is 1 over 0 Now this 5 over 0 is equal to 1 over 0 We don't know because we can't divide by 0 In our equation, we already know x is equal to 3 works But for this equation, we don't know what happens when x is equal to 0 It doesn't mean it goes on forever Infinity doesn't mean it goes on forever Infinity is not a number It's us saying that we don't know what happens It explodes Something goes haywire in the language of math 5 divided by 0 1 divided by 0 We don't know Check this is not, you know, this doesn't work So you eliminate x is equal to 0 So the only solution of this equation is x is equal to 3 Now I know I'm being a dead horse here We've done this, you know, we'll keep on working on this equation But I just wanted to point across how this stuff works And hopefully this made sense I know I've jumped over a few concepts that we will be dealing with later on Definitely when it comes to factoring But I just wanted to go through this with the cross multiplication as well