Learn about One Step Equations and Their Applications In this lesson, we will learn how to solve one-step equations. Equations are essentially two expressions, so I could have x+2=7, so there is one expression on the left, one expression on the right and there is usually an equal to sign in the middle. The way we solve the equation is we separate or alienate the variable. What we do is we figure out how to get the variable on one side and move everything else to the other side of the equal sign. The way we do that is we remember that addition and subtraction are inverse operations, and multiplication and division are inverse operations. So, if we see that with the variable something has been added or subtracted, I can do the opposite to negate that. I’ll show you what I mean with a couple of examples. Let's solve these three problems. First one says x-10=4, this is an equation. You’ve got the left hand side and you’ve got the right hand side. What we have to do is keep x on the left hand side and move everything else to the right. So, what we do have? In part A, we got x-10=4. Now, what I'm going to do is since 10 have been subtracted from the variable x, I'm going to add 10 and do it on both sides. As long as I add or subtract or multiply or divide equally on both sides of the equal two sign, we are okay. So, x-10 and +10 leaves us with x on the left. On the right hand side, 4+10 is 14, so that gives x=14. The solution of any equation is the value of the variable which makes this equation true. Let's double check. If x were 14, would this be true? Would this equation be true for x=14? Let’s see. If instead of x, I put 14, 14-10=4, that’s correct. So, the solution of this equation is x=14. Let's do part B. Part B tells us 13=-2×w which is the variable. Since I’ve got the variable multiplied by -2, let's divide by -2 on both sides. Since the variable has been multiplied by negative here, let's divide it. Do exactly the opposite. So, w multiplied by -2 and divided by -2 is just w. In this side 13÷-2 is -13/2. So, that’s the solution for w=-13/2. All we do is we keep the variable on one side and everything else on the other and remember, additions, subtraction are inverse operations, multiplication, division are inverse operations. Let's do a quick word problem. The word problem says that a person’s maximum heart rate is the highest rate in beats per minute that the heart should reach. Te way we get that is to add the person’s age to her maximum heart rate which is 220. So, the person’s age plus maximum rate equals 220. That’s the equation, age plus maximum heart rate equals 220. We need to write and solve an equation for find the heart rate of a 16-year old. So if age let's say is a plus the maximum rate is r equals 220 is the equation. Let's do this. For a 16-year old, age is 16. So, 16 plus their maximum hear rate should be 220. That’s our equation that we have to solve. How would we do that? Well, since r is the variable that we have to solve for and it looks like we’ve added 16 to it; let's subtract 16 from both sides. What do I get? R on the left hand side, 220-16 is 204, so the maximum heart rate should be 204 for a 16 year old.