## Subtitles section Play video

• Hi, I’m Rob. Welcome to Math Antics.

• In the last two Algebra videos, we learned how to solve simple equations

• that had only one arithmetic operation in them.

• But often, equations have many different operations

• which makes solving them a little more complicated.

• In this video, were going to learn how to solve equations

• that have just two math operations in them.

• one addition or subtraction operation, and one multiplication or division operation.

• And the concepts you learn in this video will help you solve even more complicated equations in the future.

• Now as you might expect, equations that have two arithmetic operations in them

• are going to require two different steps to solve them.

• In other words, to get the unknown all by itself, youll need toundotwo operations.

• But that doesn’t sound too hard, right?

• I meanwe learned how to do undo any arithmetic operation in the last two videos.

• And that’s true. But there are a couple of reason that make two-step equations a little trickier to solve.

• The first is that there are a lot more possible combinations of those two operations.

• And the second is that, when there’s more than one operation, you have to decide what order to undo those operations in.

• Uhhello! If you need to know what order to do operations in,

• just follow the Order of Operations rules!

• You DID watch that video, didn’t you?

• I sure did!

• But the Order of Operations rules tell us what order to DO operationsnot what order to UNDO them!

• UhWellthen

• could we REVERSE the order since were UN-doing operations?

• Now that’s a good idea.

• Well of course it is!

• When solving multi-step equations, that’s basically what were going to do.

• Using the Order of Operations rules in reverse can help us know what order to undo operations in,

• but it can be a little tricky actually putting it into practice.

• Soto see how it works, let’s start by solving a very simple two-step equation: 2x + 2 = 8.

• In this equation, the unknown value ‘x’ is involved in two different operations

• addition and multiplication (which is implied between the first 2 and the ‘x’)

• And to undo those two operations, we need to use their inverse operations

• subtraction and division. But the question is, which one should we do first?

• Like many things in life, the order we decide to do things in can make a big difference.

• Ah, come on!

• There’s gotta be an easier way!

• [voice from off screen] “First socks, then shoes.”

• Fortunately, in math, we have a special set of rules that tell us what order to do operations in.

• Those rules tell us to do operations inside parentheses (or other groups) first.

• And then we do exponent,

• and then multiplication and division,

• and last of all, we do addition and subtraction.

• Those are the rules you need to follow when simplifying mathematical expressions or equations.

• But solving an equation is different because we are trying to UNDO any operations

• that the unknown value is involved with so that the unknown value will be all by itself.

• So when solving equations, the best strategy is to apply those Order of Operations rules in reverse.

• Using the reverse Order of Operations is not the only way to solve a multi-step equation,

• but it’s usually the easiest way.

• Just like it’s much easier to take your shoes and socks off in the reverse order that you put them on!

• Ahhhhh! Are you sure it’s socks before shoes?

• Since the Order of Operations rules tell us to DO multiplication before we DO addition.

• We should UNDO addition before we UNDO multiplication.

• So first, we undo the addition by subtracting 2 from both sides of the equation.

• On the first side, theplus 2’ and theminus 2’ cancel each other out, leaving just ‘2x’ on that side.

• And on the other side we have 8 minus 2 which is 6.

• Next, we can undo the multiplication by dividing both sides of the equation by 2.

• On the first side, the ‘2’s cancel, leaving ‘x’ all by itself.

• And on the other side, we have 6 divided by 2 which is just 3.

• Thereweve solved the equation using the Order of Operations rules in reverse,

• and now we know that x = 3.

• That wasn’t so bad, was it?

• Let’s try solving another simple two-step equation that has division and subtraction in it: x/2 - 1 = 4.

• Again, were going to apply the Order of Operations rules in reverse

• to undo the subtraction and the division operations.

• Since we would normally DO the subtraction last, were going to UNDO it first.

• To undo the subtraction, we add '1' to both sides of the equation.

• On the first side, theminus 1’ and theplus 1’ cancel out, leaving just ‘x’ over 2 on that side.

• And on the other side, we have 4 plus 1 which is 5.

• And then, to undo thedivided by 2”, we need to multiply both sides by 2.

• On the first side, the ‘2’s cancel, leaving ‘x’ all by itself.

• And on the other side, we have 2 times 5 which is 10.

• So our answer is x = 10.

• Those examples are pretty easy, right?

• But solving two-step equations gets a bit trickier

• thanks to a little something in math calledgroups”.

• Do you remember how parentheses are used to group things in math?

• And our Order of Operations rules say we are supposed to do any operations that are inside parentheses first.

• In other words, we need to do operations that are inside of groups first.

• Well guess what?

• That means that when were solving equations and UN-doing operations,

• we need to wait to do groups LAST of all.

• To see what I mean, let’s solve this equation, which looks very similar to the first one we solved.

• The only difference is that a set of parentheses has been used to group this x + 2 together.

• And even though that might not seem like much of a change, it makes a big difference for our answer.

• That’s because, in the original equation, this first 2 is only being multiplied by the ‘x’,

• but in the new equation, it’s being multiplied by the entire quantity (or group) x + 2.

• And that’s going to change how we solve it.

• Were still going to follow our Order of Operations rules in reverse,

• but now that the x + 2 is inside parentheses (which means that it’s part of a group),

• were going to undo THAT operation last.

• Since we are supposed to DO operations in groups first, that means were going to UNDO operations in groups last.

• So in this problem, we should start by undoing the multiplication that's implied between the 2 and the group (x + 2)

• To do that, we divide both sides of the equation by 2.

• On the first side, the 2 on the top and the 2 on the bottom cancel, leaving the group (x + 2) on that side.

• And on the other side, we have 8 divided by 2 which is 4.

• That looks simpler already! And we can make it even simpler than that,

• because now that there’s nothing else on that side of the equal sign with the group (x + 2)

• we really don’t even need the parentheses any more.

• Next, we just need to subtract 2 from both sides.

• On the first side, theplus 2’ and theminus 2’ cancel out, leaving ‘x’ all by itself,

• and on the other side we have 4 minus 2, which is 2.

• So for this equation, x = 2.

• And now you can see how grouping operations differently in our equation results in different answers.

• Let’s try one more important example.

• Do you remember the second equation we solved? x/2 - 1 = 4

• In this equation, the 1 is being subtracted from the entire ‘x over 2’ term.

• But take a look at this slightly different equation.

• This looks a lot like the original equation,

• but now that the '1' is up on top of the fraction line, it’s only being subtracted from the ‘x’ and NOT the 2.

• The ‘x - 1’ on top forms a group.

• Hold on! How can the ‘x - 1’ be a group?

• I don’t see any parentheses or brackets around it.

• Ah, that’s a good question!

• In Algebra, the fraction line is used as a way to automatically group things that are above it or things that are below it.

• For example, in this fancy algebraic expression,

• everything that’s on top of the fraction line forms a group

• and everything on the bottom of the line forms another group.

• Of course, we could put parentheses there if we wanted to make it really clear, but it’s not required.

• Grouping above and below a fraction line is justimpliedin Algebra.

• Getting back to our new problem,

• now that we know that the ‘x - 1’ on the top of the fraction line is an implied group,

• as we learned in the last example, were going to wait and undo the operation inside that group last.

• So the first step is to undo thedivided by 2’ by multiplying both sides of the equation by 2.

• On the first side, the 2 on top and the 2 on the bottom will cancel out, leaving just our implied group ‘x - 1’ on that side.

• And on the other side, we have 4 times 2 which is 8.

• Next, we can undo the operation inside the group by adding '1' to both sides.

• On the first side, theminus 1’ and theplus 1’ cancel, leaving ‘x’ all by itself.

• And on the other side, we have 8 plus 1 which is 9. So in this equation, x = 9.

• AlrightAs you can see, solving two-step equations is definitely more complicated than single step equations

• because there are so many different combinations and different ways to group things.

• But if you just take things one step at a time and remember to UNDO operations using the REVERSE Order of Operations rules,

• it will be much easier.

• Just pay close attention to how things are grouped in an equation

• and be on the lookout for thoseimpliedgroups on the top and bottom of a fraction line.

• And, because there are so many variations of these two-step equations,

• it’s really important to practice by trying to solve lots of different problems.

• As always, thanks for watching Math Antics and I’ll see ya next time.

• Learn more at www.mathantics.com

Hi, I’m Rob. Welcome to Math Antics.

Subtitles and vocabulary

Click the word to look it up Click the word to find further inforamtion about it

# Algebra Basics: Solving 2-Step Equations - Math Antics

• 8 5
Yassion Liu posted on 2016/07/22
Video vocabulary