 So what if we have a linear equation that involves multiplication or division? So we'll need to figure out how to unwrap the package. We need to identify a few more inverses. If the expression is a product, multiply a by b, the inverse operation is going to be a quotient. Divide by a or divide by b, your choice. On the other hand, if the expression is a quotient, divide by a, the inverse operation is going to be a product. Multiply by a. Here we don't have a choice. We have to multiply by whatever we divided by. So for example, let's solve 5x equal to 17. So the first thing we should figure out is what type of expression we have. And this expression is a product. It's 5 times x. And so that means the inverse operation is going to be a division. We either divide by x or we divide by 5. Now, as a general rule, never divide by a variable or a variable expression. So while we do have the choice of dividing by x or dividing by 5, we don't want to make the choice divide by x. The reason is we haven't yet unwrapped the package, so we don't actually know what the variable is. So you know how you're not supposed to accept packages from people you don't know to carry on to airplanes. We have the same issue here. We don't know what's in this package x, so we don't want to divide by it because we know for absolute certain we're not allowed to divide by zero. And maybe this package has a zero in it, and we don't want to take that risk. So never divide by a variable or a variable expression, which means that we have to divide by 5. And so we'll divide both sides by 5. And so this 5x divided by 5 that cancels out the 5. And on the right-hand side our expression is going to be 17 divided by 5. And what's important to recognize here is that we have solved this equation for x because it is now in the form x equals something that doesn't involve x. As always, we really should check that our solution works. So if x equals 17 over 5, then we should be able to replace x with 17 over 5 in our equation and get a true statement. So we'll make that replacement. And this is true, so x equals 17 over 5 is a solution. So how about this equation, solve 8 times quantity x minus 7 equal to 15. So again, it's really helpful to identify what type of expression we have. So over on the left-hand side we have a product 8 times x minus 7. And since we have a product, we can divide by either 8 or x minus 7, but we don't want to divide by a variable expression, so we should divide by 8. So we'll divide both sides by 8. And now we have x minus 7 equals 15 over 8, and this expression x minus 7 is a difference. We are subtracting 7, so we should undo it by adding 7. And so we get our answer x equals 15 over 8 plus 7. And we've solved this equation because we now have it in the form x equals stuff that doesn't involve x. Now it is considered stylish to do the final arithmetic, so let's fiddle around with these numbers. And that gives us another form of the answer, x equals 71 eighths. It's important to emphasize that this answer, 15 over 8 plus 7, is a perfectly good solution. The answer 71 eighths is slightly better because it's in a nicer form, but they're the same solution. And importantly, when you go to check your solution, it turns out that this form, 15 over 8 plus 7, the un-reduced form is actually easier to work with. So we'll check our solution, x equals 15 over 8 plus 7. Every time we see x, we'll drop in 15 over 8 plus 7. And this expression 15 over 8 plus 7 minus 7 gives us 15 over 8. And we see that that's a true statement, and so our solution is 15 over 8 plus 7. Thank you very much.