Basic Math Solving Addition and Subtraction Equations

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For the next lesson, we are going to be solving equations that involve adding and subtracting.0002

To solve an equation means to solve for the unknown variable.0011

Whenever you have an equation and you have one variable only, you can solve for it.0018

Once you get the variable by itself, you are going to solve the equation.0026

In order to get the variable by itself, you are actually going to use inverse operations.0032

If you have A plus 1 equals 2, here A this is what you are solving for.0037

That means I want to get rid of this number.0050

I want to get rid of this number so that I have A by itself.0058

Some equations are easy to do; you can do it in your head.0063

I know something plus 1 equals 2; that something has to be 1.0066

A has to be 1 because 1 plus 1 equals 2.0073

But when you write it, you are going to write it like that.0076

I'm sorry... like this because you know that A is 1.0081

This is how you are going to have to write the answer.0089

When the equation gets a little bit tough, a little bit harder,0092

you want to use inverse operations to solve for this variable.0096

because once you have the variable by itself like this here, you have solved the equation.0102

If I want to solve for this variable, I have to get rid of this 1.0111

The inverse operation of addition is subtraction; it is like the opposite.0117

What is the opposite operation?--it is subtraction.0124

What is the opposite of subtraction?--it is addition.0128

Here this is A plus 1; this involves addition.0133

That means the inverse operation would be subtraction.0138

We would have to subtract this to get rid of it because 1 minus 1 equals 0.0143

That is how you get rid; that is how you make it go away.0151

But whatever you do to one side of an equal sign for an equation, you have to do to the other.0155

If I am going to subtract 1 from this, this is the left side.0162

If I subtract one here, then I have to subtract one over here too.0168

Whatever you do to one side, you must do to the other side.0172

This goes away.0178

We want it to go away because we want to get the variable by itself.0180

We want to isolate the variable; that is why we had to subtract the 1.0183

This becomes A equal to... 2 minus 1 is 1.0189

Again in order for you to solve an equation, if you can't do it in your head,0197

if you can't use mental math, you want to get the variable by itself0204

by getting rid of whatever is next to it on that side of the equal sign.0211

In this equation here, it is a +1.0216

To get rid of a +1, I need to subtract it; do the inverse operation.0220

Subtract it; because it is +1, I need to subtract 1.0226

Whatever I do to one side, I have to do to the other side.0230

This will cancel out because it will be a 0.0234

You are just going to bring this down.0237

This is the only thing left on the left side.0239

What is left on the right side of the equal sign?0242

2 minus 1, you have to solve that out; that becomes 1.0244

Once the variable is by itself, you have solved the equation.0248

Let's do a few examples; let's try it.0255

For these problems, let's just use mental math.0258

That means we are just going to do it in our head.0260

4 minus a number is 3; what do you subtract from 4 to get 3?0263

Isn't that 1?--4 minus 1 equals 3.0271

Instead of just writing 1, I want to write that my variable A is 1.0275

You would have to write it like this.0282

You are writing that the variable, the unknown value, is 1.0285

X minus 3 is 4; what number subtract 3 will give you 4?--7.0292

Instead of just writing 7, I am going to write X is 7; X equals 7.0303

Here 5 plus something equals 11; 5 plus 6.0311

Again V, the variable, equals 6.0316

26 equals 8 plus C; 8 plus what equals 26?0322

If you subtract it from here, that will be 18.0331

C equals 18 because 8 plus 18 is 26.0338

For these, we want to use the inverse operation so that we can solve.0346

That means if it is plus, I want to subtract; that is the inverse operation.0352

Inverse operation of plus is minus; inverse operation of minus is plus; the opposite.0363

I am just going to draw a line just to split my two sides, my left side and my right side.0374

I want to solve for this variable A.0382

I want to keep going until I have A all by itself on the left side.0387

Since I want this to be by itself, I have to get rid of this number here.0392

That means in order to get rid of it, since it is +3, how do I get rid of a +3?0399

I have to subtract 3; the inverse operation of plus is minus.0407

I am going to subtract it so that I can make it go away.0412

Whatever I do to one side, remember I have to do to the other side.0416

On my left side, since this is no longer there, all I have left is this A.0426

I can just write A down there.0432

Because this becomes 0, I don't have to write A plus 0.0435

A plus 0 is just A.0438

I am going to write A; then bring down the equal sign.0440

10 minus 3, I need to solve this out on the right side.0445

10 take away 3 is 7.0448

This one is an easy equation; you can just do it in your head.0452

You know that 7 plus 3 is 10.0454

But we want to be able to know how to solve equations in this way using inverse operations.0457

My answer is A equals 7.0463

The next one, -2 plus C equals 11.0468

Again I am going to draw a line through just to separate my two sides--left side, right side of the equal sign.0475

Again what am I solving for?--always know what you are solving for.0484

Here is my variable; I want it to be by itself on the left side.0488

It is not by itself; it has this number right here next to it.0493

I want to get rid of it; how do I get rid of a -2?0497

This is negative; again it is the same thing as minus.0502

Minus, negative, they are the exact same thing.0506

If this is a -2, if I owe $2, how do I get rid of that?0511

How do I make that into 0?--I have to give a +2.0517

-2 plus 2; that makes 0.0523

Whatever I do to this side, I have to do to the other side.0527

If I add 2 here, I have to add 2 here.0532

What is left on my left side?0538

This went away; this is just a +C.0539

I don't have to write a plus in front of it because plus C is the same thing as +C.0544

Even if I don't write the positive sign, I know that the C is positive still.0550

This is C equals... 11 plus 2 is 13; C equals 13.0558

For this next one, a common mistake here would be to subtract this 4 to the other side.0568

But again you are solving for the variable.0580

This time, the variable is on the right side; that is OK.0584

Just make sure that you identify the variable.0588

You want to get the variable by itself on whichever side it is on.0591

That means I want to get rid of this number here because that is on the same side of the variable.0595

The whole point is to get the variable by itself.0604

To get this by itself, let's get rid of that number; this is a +5.0609

If there is no negative sign in front of it, then it is always a positive.0614

This is 5 minus 5 to get 0.0619

Whatever I do to one side, I have to do to the other side.0624

This is a positive.0632

Again if there is no sign in front of it, it is a positive.0633

+4 minus 5; +4 minus 5.0636

With these integers, it still might be a little bit difficult to do 4 minus 5.0643

If it is, think of this as having 4 apples.0654

But again you need 5 apples.0661

If you have 4, you need 5, you are short.0665

If you need 5 apples but you only have 4, then you need 1 more.0671

Whenever you need something, whenever you don't have it, it is a negative number.0675

You can also think of this as having 4 dogs.0681

Let's say dogs are positive numbers; D is for dog; we have 4 dogs.0690

Whenever you have a negative number, that is going to be a cat.0697

We are going to have 5 cats because we have a -5.0701

A dog and a cat cancels out; those cancel out; those cancel out; and cancels out.0707

What do you have left?--you have 1; is this a positive or negative?0715

Cats are negative; that would be a -1; here this becomes -1.0721

Be careful, do not put 1; this has to be a -1.0729

If you want, you can also use a number line.0734

This is again only if you are having trouble with integers.0738

Here is a 0; I am going to start off at my first number.0742

That is 4; I am going to start here; then minus 5.0747

If I subtract, then I have to go this way; how many?--5.0753

I am going to go 1, 2, 3, 4; then I have to go one more, 5.0759

What is 1 more?--this is a -1.0766

This is not 1; 1 is right here; -1 is right there.0770

You can do it that way too.0777

Continuing, this I bring down; that went away.0784

That was the whole point--to make that go away so that this variable M will be by itself like that.0788

Now that I have the variable by itself, I have my answer.0798

This is the same thing as... if you want, you can rewrite it like this.0801

If you don't like that variable on that side,0810

since you are probably used to having variables on this left side, you can rewrite it.0812

-1 equals M; or you can say M equals -1.0819

For this next one, be careful here because the variable is here.0826

The variable is already by itself.0834

There is no need to move anything over.0837

There is no need to add, subtract, do any inverse operations.0839

We can just go ahead and solve this.0843

2 plus -2, if I have 2 of something, I take away 2.0847

It is like having 2 apples and then eating 2 apples.0854

You have 0 apples left.0856

Equals; then D; this is my answer.0860

0 is still a number; see how we have 0 right there?0870

It is still a number; D equals 0; that would be your answer.0875

Or again if you want to write the variable first, you can write D equals 0 like that.0881

They are both correct.0888

Let's do a few more; solve each equation; we are going to use inverse operations.0890

Again we are solving for B.0898

If you want, you can circle it to help you know what you are solving for and help you to see what to get rid of.0901

I am going to separate my sides with the line.0910

You don't have to draw the line; but it helps to see it.0912

This is the left side; this is the right side; you are moving this.0915

You are getting rid of it by doing the inverse operation to this side and to that side.0921

Whatever you do to one side, you must do to the other side.0928

The inverse operation of minus is plus.0933

I have to add 7 so that this will go away; add 7 here.0938

This is nothing; what is left on my left side?--on that side?0948

B equals -1 plus 7.0952

Again if the numbers are small, then you can just use the dog-cat example.0959

You can also say you need 1 apple; you have 7.0964

After you use that 1 that you need, how many do you have left?0974

You have 6 left.0978

To show you the dog and cat example again, a negative number is a cat.0981

That is 1 cat; then 7 dogs; 1, 2, 3, 4, 5, 6, 7.0988

7 Ds represents a +7; this cancels; how many dogs do you have left?0998

1, 2, 3, 4, 5, 6; this is 6; is that positive or negative?1006

Dogs are positive; it is +6; that is my answer.1011

Then here again you are solving for E; you can separate the sides.1020

I have to get rid of whatever is next to it which is the 4.1026

You don't have to get rid of pluses because plus is the same thing as positive.1030

Just like minus is the same thing as negative, a plus is the same thing as a positive.1035

Here this is a +4; there is no negative sign in front of it.1042

It automatically gets a positive; if that helps, you can write that in.1047

To get rid of a +4, you have to subtract 4; you have to take 4 away.1052

Whatever you do to one side, you have to do to the other side.1057

This becomes nothing; E is left only on that side which is what we want.1063

Equals; this is dog, dog, cat, cat, cat, cat; cancel, cancel.1069

This becomes 2; cats are negative; E is -2.1081

The next one, circle the variable.1092

Here this is what I have to get rid of because it is next to the variable on that side of the equal sign.1101

To get rid of a -6, I have to add 6; that is the inverse operation.1108

Whatever I do to one side, I have to do to the other side.1113

This goes away; P by itself now equals -5 plus 6; 1.1118

If you borrowed 5, you have 6, so after paying that 5 back, you have 1 left over.1134

For this one, you can circle and draw the line.1147

You are getting rid of the 3, not the 8, because the 3 is on the same side of the variable.1153

The whole point is to get the variable by itself.1159

Again this is a +3; I need to subtract 3 to make this 0.1163

Whatever I do to one side, I have to do to the other side which is over here.1169

Be careful, you don't do it to the same side.1173

It has to be to the other side.1176

That is why you draw this line just to make it easier to see this side and that side.1179

Went away; what is left?--my variable equals 5.1187

For these, we are going to translate to an equation first.1200

Then we are going to solve them.1203

The sum of A... this is the variable A... and 8 is -1.1206

Sum we know is plus of A and 8.1216

That means we are going to add A and 8 together.1222

A plus 8, is means equals, -1.1226

To solve this, again we are going to solve for A.1235

Separate the two sides to get rid of this because that is still on the same side.1243

Subtract it; that is the inverse operation.1251

Whatever I do to this side, I have to do to the other side.1257

Went away; A is left by itself; equals -1 minus 8.1263

Here is a negative; here is a negative.1271

You have 1 cat; you have 8 more cats.1273

How many cats do you have total?--9 cats.1276

Cats we know are negative so it has to be a negative number.1281

There is my answer; A is -9.1286

The next one, 9 minus A is 7; 9 minus A equals 7.1293

I am solving for this.1309

For this one, we don't have to use the inverse operation.1315

If you can solve it in your head, if it is easy, then you can just go ahead and do that.1319

We know 9 minus what equals 7?--that is 2.1324

Just be careful that you are not going to just write 2 as your answer.1329

If you just write 2, you have to identify it as your variable.1333

That is what you found A to be.1338

You want to write A equals 2 because 9 minus 2 equals 7.1344

Next one, K more than 14 is 20.1354

We know more than is plus; this is plus.1359

But then I see this word here.1365

Remember whenever you see that word, you have to switch them.1367

You have to write it in the opposite order.1371

Instead of K plus 14, you are going to say 14 plus K is 20.1375

Again you are solving for K; you can just do this in your head.1386

You know that 14 plus 6 more is going to give you 20.1392

You can say K equals 6.1396

Or if you want, you can just practice doing the inverse operation.1401

You are going to subtract 14 because this is a +14.1405

Whatever you do to one side, you have to do to the other side.1409

Goes away; K is left by itself which is what you want.1415

Equals, this is 6.1419

The last one, 5 less than Q is 11; 5 less than Q is 11.1429

Less than we know is minus; but then again here is that word.1438

It is going to be Q minus 5 equals 11.1445

A number Q, if you take 5 away, is going to be 11.1453

We know Q is going to be 16.1459

Again just to show you the inverse operation, I am solving for Q so get rid of everything on that side.1463

You are going to add 5 to get rid of it.1471

Whatever you do to one side, you have to do to the other side.1474

You are going to have Q equal to 16.1480

That is it for this lesson; thank you for watching Educator.com.1490