Solving Two Step Equations Algebra Equations

Welcome to Math with Mr. In this video, I'm going to cover how to solve two-step equations. We have four example problems on your screen there that we're going to go through together in order to get this down. Now, remember, when we have an equation with variable, our goal is to isolate that variable or get it by itself in order to solve. And we also need to remember, whatever we do to one side, we must do to the other side of the equation. We have to keep it balanced. So, let's jump right into number one and solve some two-step equations. So, for number one, we have 2x - 6 = 10. So, again, we want to isolate that get it by itself. So, like to think of it as we need to reverse the order or undo this side of the equation so we get that by itself. And we're going to use the reverse order of operations in order to do so. So, we have 2 * that and then we subtract 6. So, reverse order of operations, this subtraction of 6 needs to come first. So, how do we get rid of that 6 from the left side? Well, we can add 6. That will cancel those 6s out or give us 0. So, remember, whatever we do to one side, we have to do to the other. So, if we add 6 to the left, we need to add 6 to the right. -6 or -6 + 6 gives us that 0. And 10 + 6 is 16. So, on the left side, we're left with 2 * or 2x. So, we don't have the variable completely isolated yet, but we're almost there. So, we have 2 * So, how do we get rid of that 2? We need to either make it 0 or 1. So, the opposite of multiplying by 2 would be dividing by 2. That would give us 1x on that side, which is the same as just So, let's divide both sides by 2. and that leaves us with = 16 / 2 is 8. Now, let's plug in that 8 into the originally original equation and see if we get the correct answer. So, 2 * 8 - 6 = 10. It's always good idea to see if that answer works out. 2 * 8 is 16. - 6 does give us that 10. So, we have the correct answer, = 8. So, for number two, we have / 5 + 8 = 11. So, we need to get that by itself. So, let's do the reverse order of operations to undo the left side of the equation. So, let's get rid of that 8 first. So, we have + 8. So, the opposite, let's subtract 8 from both sides to begin to isolate the So, positive 8 and negative 8 there, -8, gives us 0. And 11 - 8 gives us 3. So, on the left side, we're left with / 5. So, let's get rid of the 5 from the left side. What's the opposite of divided by 5? Dividing by 5. Well, multiplying by 5. So, let's multiply both sides by 5. by 5 by 5 and we get equals Well, 3 * 5 is 15. We isolated the variable and it equals 15. So, on the left-hand side, just want to mention we had / 5 that last step and we times by 5, which would technically give us over 1 or / 1, which is just This is isolating the variable right here. If you get to multiplying that variable by 1 or dividing that variable by 1. So, let's plug in that 15 and see if we get the correct answer here. So, I'm running out of room little bit. I'll fit it in here. So, 15 / 5 is 3. Bring down our 8 and we end up with 3 + 8, which gives us the 11 we wanted. So, let's go over to number three here, where we have 7 = 16 3e. So, the equation looks little different than numbers one and two. We have the variable on the right-hand side, but it's the same exact thing that we did for numbers one and two. So, we need to isolate that So, undo that right side of the problem. So, let's get rid of the 16 first. So, we have positive 16 on the right-hand side. So, the opposite would be subtracting 16 in order to get rid of it. Let's do -16 on the left-hand side as well. So, 16 16 gives us that 0. 7 - 16 gives us negative 9. We're left with -3e on the right side. So, that's multiplication. So, we need to do the opposite of multiplication in order to get the by itself. So, let's divide both sides by -3. -9 / -3 gives us positive 3. And we're left with over 1, which is the same thing as just We isolated the variable. So, = 3. Let's plug it back in and see if that works. 3 * 3 is 9. Bring down our 16. 16 - 9 does give us that 7 that we were looking for on the left-hand side of that equation. So, we were correct, = 3. And lastly, number four. So, we have some parentheses in this one and we need to get by itself or isolate the variable So, we have 2 * (y - 8) = 24. So, we need to do the opposite. Remember, we need to undo that side, the left-hand side of the equation. And we're going to actually divide both sides by 2 to undo that 2 that is outside of the parentheses. So, 2 / 2 is 1. That gives us 1 outside of the parentheses there, which is just going to leave us with - 8, because anything * 1 is just that number or expression itself. So, we just have 8. And then 24 / 2 is 12. So, now we have - 8 = 12. So, we need to get rid of that -8. Undo that part of the left-hand side of the equation in order to isolate the So, we need to add 8 to both So, -8 and +8 gives us 0. Those cancel out. So, we're left with And 12 + 8 gives us 20. So, equals 20. Let's plug it back into the equation to see if this gives us the answer 24 that we're looking for. 20 - 8 is 12. Bring down the 2 outside of the parentheses, which means multiplication, and 2 * 12 does give us that 24 that we wanted. So, there you have it. There's how you solve two-step equations. Hopefully, that helped. Thanks so much for watching. Until next time, peace.