## Subtitles section Play video

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

• In our last Algebra video, we learned that Algebra involves equations

• that have variables or unknown values in them.

• And we learned that solving an equation means figuring out what those unknown values are.

• In this video, were going to learn how to solve some very simple

• Algebraic equations that just involve addition and subtraction.

• Then in the next video, well learn how to solve some simple equations involving multiplication and division.

• Are you ready?… I thought so!

• Okayso if youve got an equation that has an unknown value in it,

• then the key strategy for solving it is to rearrange the equation

• until you have the unknown value all by itself on one side of the equal sign,

• and all of the known numbers on the other side of the equal sign.

• Then, youll know just what the unknown value is.

• But, how do we do that? How do we rearrange equations?

• Well, we know that Algebra still uses the four main arithmetic operations

• (addition, subtraction, multiplication and division)

• and we can use those operations to rearrange equations,

• as long as we understand one really important thing first.

• We need to understand that an equation is like a balance scale.

• Youve seen a balance scale, right?

• If there’s the same amount of weight on each side of the scale,

• then the two sides are in balance.

• But, if we add some weight to one side...

• then the scale will tip.

• The two sides are no longer in balance.

• An equation is like that.

• Whatever is on one side of the equal sign MUST have exactly the same value

• as whatever is on the other side.

• Otherwise, the equation would not be true.

• Of course, that doesn’t mean that the two sides have to look the same.

• For example, in the equation 1 + 1 = 2,

• 1 + 1 doesn’t LOOK the like the number 2,

• but we know that 1 + 1 has the same VALUE as 2,

• so 1 + 1 = 2 is in balance. It’s a true equation.

• The reason we need to know that equations must be balanced

• is because when we start rearranging them, if we are not careful,

• we might do something that would change one of the sides more than the other.

• That would make the equation get out of balance and it wouldn’t be true anymore.

• And if that happens, we won’t get the right answer when we solve it.

• That sounds pretty bad, huh? So how do we avoid that?

• How do we avoid getting an equation out of balance?

• The key is that whenever we make a change to an equation,

• we have to make the exact same change on both sides

• That’s so important, I’ll say it again.

• Whenever we do something to an equation,

• we have to do the same thing to BOTH sides.

• For example, if we want to add something to one side of an equation,

• we have to add that same thing to the other side.

• And if we want to subtract something from one side of an equation,

• then we have to subtract that same thing from the other side.

• And it’s the same for multiplication and division.

• If we want to multiply one side of an equation by a number,

• then we need to multiply the other side by that same number.

• Or if we want to divide one side of an equation by a number,

• then we have to divide the other side by that number also.

• As long as you always do the same thing to both sides of an equation,

• it will stay in balance and your equation will still be true.

• Alright, like I said, in this video, were just going to focus on equations involving addition and subtraction.

• And here’s our first example: x + 7 = 15

• To solve for the unknown value ‘x’,

• we need to rearrange the equation so that the ‘x’ is all by itself on one side of the equal sign.

• But what can we do to get ‘x’ all by itself?

• Well, right now ‘x’ is not by itself because 7 is being added to it.

• Is there a way for us to get rid of that 7?

• Yes! Since seven is being added to the ‘x’, we can undo that by subtracting 7 from that side of the equation.

• Subtracting 7 would leave ‘x’ all by itself because ‘x’ plus 7 minus 7 is just ‘x’.

• Theplus 7’ and theminus 7’ cancel each other out.

• Okay great! So we just subtract 7 from this side of the equation and ‘x’ is all by itself.

• equation solved, right?

• WRONG! If we just subtract 7 from one side of the equation and not the other side,

• then our equation won’t be in balance anymore.

• To keep our equation in balance, we also need to subtract 7 from the other side of the equation.

• But on that side, we just have the number 15.

• So we need to subtract 7 from that 15.

• And since 15 - 7 = 8, that side of the equation will just become 8.

• There, by subtracting 7 from BOTH sides, weve changed the original equation (x + 7 = 15)

• into the new and much simpler equation (x = 8) which tells us that the unknown number is 8.

• We have solved the equation!

• And to check our answer, to make sure we got it right,

• we can see what would happen if we replaced the unknown value in our original equation with the number 8.

• Instead of x + 7 = 15, we’d right 8 + 7 = 15,

• and if that’s true, then we know we got the right answer.

• Pretty cool, huh?

• Let’s try another one: 40 = 25 + x

• This time, the unknown value is on the right hand side of the equation.

• Does that make it harder?

• Nope. We use the exact same strategy.

• We want to get ‘x’ by itself, but this time ‘x’ is being added to 25.

• But thanks to the commutative property, that’s the same as 25 being added to ‘x’.

• So, to isolate 'x', we should subtract 25 from that side of the equation.

• But then we also need to subtract 25 from the other side to keep things in balance.

• On the right side, x plus 25 minus 25 is just x

• The minus 25 cancels out the positive 25 that was there.

• And on the other side we have 40 minus 25 which would leave 15.

• So the equation has become 15 = x, which is the same as x = 15.

• Again, weve solved the equation.

• So, whenever something is being added to an unknown,

• we can undo that and get the unknown all by itself

• by subtracting that same something from both sides of the equation.

• But what about when something is being subtracted from an unknown,

• like in this example: x - 5 = 16

• In this case, ‘x’ is not by itself because 5 is being subtracter or taken away from it.

• any ideas about how we could get rid of (or undo) thatminus 5’?

• Yep! To undo that subtraction, this time we need to ADD 5 to both sides of the equation.

• Theminus 5’ and theplus 5’ cancel each other out and leave ‘x’ all by itself on this side.

• And on the other side, we have 16 + 5 which is 21.

• So in this equation, x equals 21.

• Let’s try another example like that: 10 = x - 32.

• Again the ‘x’ is not by itself because 32 is being subtracted from it.

• So to cancel thatminus 32’ out, we can just add 32 to both sides of the equation.

• On the right side, theminus 32’ and theplus 32’ cancel out leaving just ‘x’.

• And on the left we have 10 + 32 which is 42. Now we know that x = 42.

• Okay, so now you know how to solve very simple equations like these

• where something is being added to an unknown or where something is being subtracted from an unknown.

• But before you try practicing on your own,

• I want to show you a tricky variation of the subtraction problem

• that confuses a lot of students.

• Do you remember how subtraction does NOT have the commutative property?

• If you switch the order of the subtraction, it’s a different problem.

• Suppose we get a problem, where instead of a number being taken away from an unknown,

• an unknown is being taken away from a number.

• What do we do in that case?

• Well, we still want to get the unknown all by itself,

• but it’s a little harder to see how to do that.

• In this problem (12 - x = 5) the 12 on this side is a positive 12,

• so we could subtract 12 from both sides.

• That would get rid of the 12,

• but the problem is that wouldn’t get rid of this minus sign.

• That’s because the minus sign really belongs to the ‘x’ since it’s the ‘x’ that is being subtracted.

• Subtracting 12 would leave us withnegative x’ on this side of the equal sign,

• which is not wrong, but it might be confusing if you don’t know how to work with negative numbers yet.

• Fortunately, there’s another way to do this kind of problem that will avoid getting a negative unknown.

• Instead of subtracting 12 from both sides, what would happen if we added ‘x’ to both sides?

• Can we do that? Can we add an unknown to both sides?

• Well sure! why not?

• We can add or subtract ANYTHING we want as long as we do it to both sides!

• And when we do that, theminus x’ and theplus x’ will cancel each other out on this side.

• And and the other side, we will get 5 + x.

• Now our equation is 12 = 5 + x.

• And you might be thinking, “but why would we do that? That didn’t even solve our equation!”

• That’s true, but it changed it into an equation that we already know how to solve.

• Now it’s easy to see that we can isolate the unknown just by subtracting 5 from both sides of the equation.

• That will give us 7 = x or x = 7.

• It just took us one extra step to rearrange the equation,

• but then it was easy to solve.

• Okay, that’s the basics of solving simple algebraic equations that involve addition and subtraction.

• You just need to get the unknown value all by itself,

• and you can do that by adding or subtracting something from both sides of the equation.

• And this process works the same even if the numbers in the equations are decimals or fractions.

• And it also works the same no matter what symbol you are using as an unknown.

• It could be x, y, z or a, b, c.

• The letter being used doesn’t matter.

• Remember, when it comes to math,

• it’s really important to practice what youve learned.

• So be sure to try solving some basic equations on your own!

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