For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Solving Addition and Subtraction Equations

#### Related Links

- To solve an equation means to solve for the unknown variable
- Use inverse operations to get the variable by itself
- Inverse operation of addition is subtraction
- Inverse operation of subtraction is addition
- Whatever you do to one side of an equal sign, you must do to the other side

### Solving Addition and Subtraction Equations

5 - a = 2

30 = 3 + x

y + 5 = 23

- y + 5 - 5 = 23 - 5
- y = 23 - 5

- 5 + x = 14

- - 5 + 5 + x = 14 + 5
- x = 14 + 5

5 + x = 12

- 5 - 5 + x = 12 - 5
- x = 12 - 5

b - 9 = 17

- b - 9 + 9 = 17 + 9
- b = 17 + 9

8 + z = 14

- 8 - 8 + z = 14 - 8
- z = 14 - 8

x - 9 = - 12

- x - 9 + 9 = - 12 + 9
- x = - 12 + 9

x more than 12 is 32

- x + 12 = 32
- x + 12 - 12 = 32 - 12
- x = 32 - 12

The sum of 3 an y is 15

- 3 + y = 15
- 3 - 3 + y = 15 - 3
- y = 15 - 3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Solving Addition and Subtraction Equations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Solving Equations 0:08
- inverse Operation of Addition and Subtraction
- Extra Example 1: Solve Each Equation Using Mental Math 4:15
- Extra Example 2: Use Inverse Operations to Solve Each Equation 5:44
- Extra Example 3: Solve Each Equation 14:51
- Extra Example 4: Translate Each to an Equation and Solve 19:57

### Basic Math Online Course

### Transcription: Solving Addition and Subtraction Equations

*Welcome back to Educator.com.*0000

*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 itself*0204

*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

1 answer

Last reply by: April Dutollo

Thu Jul 30, 2015 9:14 PM

Post by April Dutollo on July 30, 2015

On example 4 (second question), if you add nine to both sides through inverse operation you would get a negative 2. Can some one explain what I'm doing wrong?

2 answers

Last reply by: Milan Ray

Tue Apr 15, 2014 10:52 AM

Post by Ramez Hajelsawi on March 17, 2013

it really depends on what a represents dose'nt it?

1 answer

Last reply by: Milan Ray

Tue Apr 15, 2014 9:45 AM

Post by Ramez Hajelsawi on February 21, 2013

How does a+1=2?