WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to be solving division equations.
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Just like the other equations that we were solving in the previous lessons,
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we are going to use inverse operations to get the variable by itself.
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The whole point of solving equations is to solve for the variable.
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What does the variable equal?--what is the value of the variable?
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For this one, the inverse operation of division is multiplication.
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The opposite operation, the opposite of division is multiplication.
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Again we are just going to solve for the variable just using mental math.
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That means 3 equals a number divided by 2.
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Don't forget, right here, this fraction also means divide.
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It is the top number divided by the bottom number.
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A divided by 2 is 3; what is A?
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What number if you divide it by 2 is going to give you 3?
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I know that 6 divided by 2 is 3.
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Again instead of writing just 6, you have to write that the variable A is equal to 6.
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Same thing here; a number divided by 3 is going to give you 5.
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15 divided by 3 is 5; that means the variable D is equal to 15.
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A number divided by 4 is 4; 16 divided by 4 is 4.
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That means I have to make B equal to 16.
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Then 100 divided by a number is going to give you 10.
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What is K?--K has to be 10 because 100 divided by 10 is 10.
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Now for these examples, we are going to solve for the variable using the inverse operation.
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I am going to circle the variable just like I did for my other lessons and then separate the sides.
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Again this is M divided by 4.
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If I have a number on the bottom and if I multiply this by 4, a +4 is the same thing as 4/1.
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4 is the same thing as 4/1; I could put 1 under any number.
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If I need to turn this into a fraction, I can put a 1 under it.
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4 divided by 1; what is 4 divided by 1?--isn't that 4?
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Remember this also means divide; 4 divided by 1 is 4.
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If you want, if it helps, you can put it over 1.
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Then if you remember, to multiply fractions, this is M times 4 which is M times 4 or you can write 4M.
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Remember if you have a number times a variable, you can just write it together like that.
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Over... this number times 1 which is 4.
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If you have the same number on top as the bottom, they will become 1.
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4 divided by 4 is 1.
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That is why the inverse operation, if this is M divided by 4, the opposite of divide is multiply.
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If I want to get rid of this 4 down here, then I have to multiply the 4.
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Again I am using the inverse operation.
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Just in the same way, this 4 is on this side this time.
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But it is the same thing; 4/1.
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Or you can leave it as 4; or you can put it over a 1.
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Times M/4; remember this becomes that same exact thing, 4M/4 because this times this is that.
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1 times 4 is 4; 4/4 makes a 1; this is 1M.
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If you remember, 1M is the same thing as M.
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Here inverse operation of divide is to multiply.
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If you multiply when it is divided from the variable, they will cancel out.
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It will go away.
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If you don't understand this, what I did here, just know that if you have to divide
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or if this is M divided by 4, then you have to multiply it so that it will go away.
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Again whatever I do to one side of the equal sign, I have to do to the other side.
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Since I multiplied 4 to this side, I have to multiply 4 to this side.
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You can write it like this for now.
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Or the best way to show that you are going to multiply two numbers is to write them in parentheses.
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What is left on the left side?
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This side, all I have left is the M which is what I want.
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I wanted to get rid of this 4; that is why I multiplied it.
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Equals -3 times 4; remember... I have a negative times a positive.
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Whenever you are multiplying or dividing, if you only have one negative sign, your answer becomes a negative.
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You are going to multiply these two numbers just the same way.
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3 times 4 is 12.
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It is a -12 because I only see one negative sign.
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Remember one negative, your answer becomes a negative.
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If you are multiplying two negative numbers, then those negative numbers pair up to become a positive; a plus.
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Then this is M equals -12; I have the variable by itself.
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So I am done; I solved the equation.
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Again next one, I am going to circle the variable.
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That is my goal, to make the variable by itself.
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I am going to separate the two sides like that.
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This is A divided by 7.
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If it is A divided by 7, the inverse operation is multiply.
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I have to multiply this whole side by 7.
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But these will cross cancel; they will become a 1.
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Whatever I do to one side, I have to do to the other side.
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7 times 6 is 42; on my left side, I get 42; then my equals.
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On my right side, I have only A left because remember I got rid of that 7.
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Once I have the variable by itself and I have the number, I am done.
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That is my answer.
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The third one, I am going to use a different color; solve for B.
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Again this is B divided by -3; it is divided by -3.
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I still have to get rid of this whole number right here.
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Inverse operation, multiply this by -3; that way these will cancel out.
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Whatever I do to one side, I have to do to the other side.
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I have to multiply this by -3.
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Then on this side, I only have a B left; equals... my right side.
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I have to solve this out; 10 times -3; 10 times 3 is 30.
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How many negative signs do I see?--I only see one.
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That means my answer is going to be negative; B equals -30.
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This last one, again solve for X; I am going to circle it.
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Separate my sides; X divided by 5; inverse operation is to multiply.
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Multiply this side; that way that number will go away.
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Whatever I do to one side, I have to do to the other side.
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What is left on this side?--X is left; equals... 8 times 5 is 40.
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I only have one negative sign; that means my answer is going to be negative.
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That is it; that is my answer.
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For these, we are going to determine if -6 is the solution of the equation.
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Here is my variable.
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I want to know if -6 can be M or if M can be -6.
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-6 divided by 2; is that 3?-- -6, I am going to replace it.
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I am going to write it instead of M because I am trying to see if M is going to be that number.
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I am just going to substitute it in; equals 3; is this true?
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I know that 6 divided by 2 is 3; but is -6 divided by 2, 3?
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No, because when you have a negative divided by a positive,
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you only see one negative, that makes the answer a negative.
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In this case, this is no or false.
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This one, I am just going to write no.
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The next one, here is my variable; 6 over... in place of the variable, -6.
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I know that 6 divided by 6 is 1; is 6 divided by -6, -1?
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Only one negative sign when you are dividing numbers; that makes this negative.
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So this one is yes; this one is true.
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Here -18 equals -6/4; does -6 divided by 4 equal -18?
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No, so this one is no.
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Let's solve each equation.
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We are going to use the inverse operations to solve each of the equations.
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The first one, I am going to circle my variable.
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I am going to separate my sides; be careful here, this is A plus 11.
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What is being used?--a plus; what is the inverse operation of plus again?
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Inverse operation of plus is minus; the inverse operation of minus is plus.
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What about times?--what is the inverse operation of times?--divide.
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And the inverse operation of divide is times.
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Since this is A plus 11, and I know I have to get the variable by itself,
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I have to get rid of everything that is next to the variable.
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I have to use the inverse operation of plus which is minus.
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That means I have to subtract this number 11 because +10 minus 11, that makes 0; that goes away.
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Whatever I do to one side, I do to the other; -4 minus 11.
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Be careful here; remember we are not multiplying; we are not dividing.
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Even though you see two negative signs, it doesn't make it go away; only when you multiply or divide.
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When it comes to adding and subtracting, you can think of dogs and cats.
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You can think of money; it is like saying you borrowed $4.
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Then you borrowed another $11; whenever you see a negative, you are borrowing.
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You borrow 4; you borrow 11; how much do you owe?
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You owe 15; that is a negative because you still owe.
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Whenever you don't have something, it is a negative.
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Bring down that equal sign; then on this side, what is left?
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Only the variable because whatever was here, we got rid of; that number that was there.
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So this is it; this is the answer.
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The whole point, the goal is to get the variable by itself.
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The next one; circle the variable; separate my sides; this is N minus 8.
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I know I have to get rid of this number because it is next to the variable.
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Inverse operation of minus is plus.
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That means to get rid of this ?A, I have to add A to make it go away so the variable can be by itself.
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Then whatever you do to one side, you have to do to the other side.
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It is the right side; only the variable is left.
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Equals... this side, the right side... 28; 20 plus 8 is 28.
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That is my answer; N equals 28.
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Solving for my variable of E; separate my sides; here this is 9 times V.
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If they are stuck together like that, that is a times; 9 times V equals -81.
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Since it is multiplied together, I have to use my inverse operation which is divide.
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I have to divide the 9 to get rid of it so that the variable can be by itself.
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Then same thing; whatever you do to one side, you have to do to the other side.
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If you did it to the left side, then you have to do it to the right side.
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From here, this is left with V; bring down the equal sign.
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Then 81 divided by 9; don't forget that this is divide.
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81 divided by 9 is 9; but then you have a negative.
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Negative divided by a positive, you only see one negative.
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In this case, only when you multiply or divide, remember.
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You are dividing now; one negative gives you a negative answer.
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That is my answer; that is it.
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The last one, D divided by -12 equals 3.
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I am going to circle my variable; separate my sides.
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This is D divided by -12; the inverse operation of divide is multiply.
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To get rid of this number here, because again we need D to be by itself.
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I need to multiply this number; make sure you divide the -12.
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The number is -12; you are multiplying -12; that cross cancels out.
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Whatever you do to one side, remember you have to do to the other side; 3 times -12.
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Again the best way to write two numbers being multiplied is to write it in parentheses.
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Can write that in parentheses too.
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On this side, on my left side, I have D left by itself.
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Equals... the right side, it is 3 times -12; first 3 times 12 is 36.
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Remember the number stays the same; I have only one negative sign.
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That makes this because it is multiplied; D is -36.
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That is it for this lesson; thank you for watching Educator.com.