 Suppose someone ships you an item. Since the item is packaged, you don't know what's in it. To find out, you have to open the package. This means undoing everything that was done to the item. And here's an important idea. To unwrap a package, you have to undo the last thing first. Similarly, the unknown in an equation is like an object that's been wrapped for shipping. To determine the unknown, you have to unwrap the package. Every arithmetic operation has an inverse operation that undoes it. Add n can be undone by subtract n. And likewise, subtract n can be undone by add n. Similarly, multiply by n can be undone by divide by n. And surprisingly enough, divide by n can be undone by, wait for it, multiply by n. And it's helpful to keep in mind there are situations where we do have a choice, and if possible, avoid operating with the variable. Now, an equation begins with a claim that two expressions are equal. But in math and in life, we can only maintain equality if we treat both sides the same. So if we do something to one side, we must do it to both sides. For example, let's solve x plus 15 equals 35. So our first thing to notice is the expression x plus 15 is a sum. Add 15 to x. Since this is an add, we can undo it. To undo add 15, we should subtract 15. And remember, if it's not written down, it didn't happen. So we'll start with our equation. We'll subtract 15, but we have to maintain equality, so we have to treat the two sides the same. We'll also subtract 15 from the right, and we find our solution. Or say we want to solve this equation for z. So our expression involving z is a subtraction, namely, subtract 11. To undo subtract 11, we should add 11. So again, if it's not written down, it didn't happen. Starting with our equation, we'll add 11 and get our solution. Or we can solve 8x equals 48. The expression involving x is a product, multiply x by 8. So undo a multiply by 8, we divide by 8, and we should record this as 48 divided by 8. But we often write this as a fraction, like 48 8s. And that comes from the following idea. As long as b is not equal to 0, then the quotient a divided by b can be written as a fraction ab. And so instead of writing 48 divided by 8, we can write the fraction 48 8s. Of course, since it is a division, we can actually perform the division and get our solution. It's helpful to keep in mind that equivalence between a fraction and a division, if we want to solve t6 equal to 3, remember t6 is the same as t divided by 6. And so the expression involving t is a quotient, divide by 6. So to undo a divide by, we multiply by 6. Now to simplify this, remember that if we multiply any fraction by its denominator, then we can remove the common factors and simply end up with the numerator.