 Suppose you get a package and open it. If the object is still wrapped, you continue unwrapping. Similarly, an unknown might be subjected to several operations. And always remember, undo the last thing. For example, suppose we want to solve 12 minus x is equal to 7. So the expression 12 minus x is a difference. We are subtracting x, so we can undo this by adding x. Now the expression 7 plus x is a sum, add x, so we could undo it by subtracting x. But if we do that, this would give us, which is where we started. So here it's helpful to remember a key property of addition, a plus b is equal to b plus a. Since addition is commutative, 7 plus x can be read as either add x to 7 or add 7 to x. So we can undo add 7 by subtracting 7. So remember that the last thing we do is always going to be determined by the order of operations. So in this expression 6x plus 5, the order of operations requires we first multiply by 6 and then add 5. So the last thing we do is to add 5, and so to solve we begin by subtracting 5. Now our left-hand side 6x is a product multiplied by 6, so to undo that we divide by 6. And we can do the arithmetic at the end, 366 is the same as 6. Now some of this arithmetic can get a little complicated, and so it's worth pointing out the value of procrastination. Wait a minute, that should have been taken out. Let's ignore that for a second. So the important idea here is we can leave the arithmetic to the end if the arithmetic is going to get too complicated for us. Remember our focus is on solving the algebraic equation. The arithmetic we can do when we do it. This is most useful if we have to deal with fractions or decimals. So here we see that our order of operation says that our variable x first has 4 subtracted because that's in parentheses. Then the result is multiplied by 5, then 1 third is added. So the last thing done is to add 1 third, so we begin by subtracting 1 third. And again, while we could do that subtraction 11 minus 1 third, let's just go ahead and record that as the arithmetic expression we need to evaluate. Now in our expression the last thing done is to multiply by 5, and so we undo this by dividing by 5. And again we could do the fraction arithmetic, but remember for now for b not equal to 0, the equation a divided by b can be written as the fraction a beats. And so we'll divide both sides by 5 and get our fractional expression. Finally, the expression is a difference subtract 4, so to solve we add 4. And this gives us an expression, and we can't avoid fractions forever. Well, actually we could. This is a perfectly reasonable answer. It's a numerical expression. All of the algebra has been completed at this step, but if we do want to turn this into a dice form we can leave that fraction arithmetic to the end and simplify to get...