# How to solve linear equations

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### Description

An eight-lesson course that teaches kids how to solve equations!

### Concepts

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• #Scripts:205

### Text Snippets

• equations! what fun!
• sarcasm intended
• but the only thing in the minds of some of you guys right now might be…
• "what the heck are equations?"
• well, let me give you an example:
• see, an equation is basically telling you what x- or any other variable- is equal to.
• so what's a variable?
• a variable is a letter representing a number that can change. for example, in that equation above, x is equal to 5.
• i’ll explain in the next lesson how i figured that out.
• back to variables, the variable x could equal something totally different in another equation, like 10,000,000,000,000.
• so what exactly do we do with these “equations?”
• well, we find the variable!
• sorry, kids, it’s not gonna be that easy.
• so how do we do it?
• i’ll explain the basics in the next lesson!
• we will rock you music
• take me out for the ball game music
• easy rider music
• chivalrous music
• my name is ethan the math demon
• i know that sounds kind of cheesy, but since a lot of your school career is spent watching cheesy videos, just deal with it
• so guess what i'm here to do today?
• i'm here to teach you how to solve equations!
• let's get going!
• Screen Shot 2017-06-22 at 4.41.13 PM
• Screen Shot 2017-06-22 at 4.41.20 PM
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• there is one central rule to solving equations
• yeah, i know rules can be stupid and annoying, but this one’s actually really important.
• basically, if you want to do something to one side of the equal sign in the equation…
• you have to do the same thing to the other!
• think of it like a scale- if you want to keep it equal, you have to add things that weigh the same on both sides.
• we can prove that this works using an example with numbers that aren’t variables.
• if we add 2 to both sides…
• they both equal five!
• so the equation is still correct because yes, 5 does equal 5
• some of you might be wondering right now what this has to do with solving equations. well, in order to solve equations, we will need to “undo” some operations.
• after hearing that, a lot of you guys might be like:
• “‘undo’ an operation? what the heck does that mean?”
• well, in order to know what x is, we have to have the equation say x = something, right?
• let’s go back to our previous example
• right now it doesn’t say what x equals, it says what x + 3 equals.
• so in order to see what x equals, we would need to get rid of the 3, right?
• and if you want to get rid of a number...
• you need to subtract it by itself!
• so we need to subtract 3 by 3 to get rid of the 3 and have only the x
• so now it’s just x =
• yay! we made it into x =
• but wait! there’s more!
• remember how i said at the beginning of the lesson that whatever you did to one side of the equation, you had to do to the other?
• well, since we subtracted 3 from the x side, we need to subtract 3 from the other side!
• so it would be x = 8 - 3
• so ultimately it would become x = 5
• huzzah! we did it!
• now let’s try a problem with subtraction, like this one:
• how would we do it?
• well, let’s think in the opposite way we were thinking in that first problem. right now, 3 is being subtracted from x, instead of added.
• if you were subtracting a number from another number (x), what would you do to get it back?
• you would add it back!
• so we would add back 3 to x after we subtract 3
• and it would still be x
• so right now we’ve added 3 to the “x” side of the equation.
• but remember! we still need to add 3 to the other side of the equation.
• so it would be: x = 8 + 3
• you could do this faster by adding or subtracting to both sides at once, like this:
• but until you get stronger at solving equations, make sure you do all your work one step at a time and show all your work so that you don’t accidently forget to add/subtract something to one side!
• now that you’ve learned how to do it, go and solve equations on your own!
• there are five practice problems waiting for you.
• have fun, and may the odds be ever in your favor!
• you've completed lesson 1!
• after the last lesson, we all should know how to solve an equation if something is being added to or subtracted from the variable.
• but what if the variable was being multiplied or divided by something?
• you’ll see that the 3 is attached right to the x. that means that they are being multiplied by each other.
• when solving equations, we don’t use the multiplication sign, because that looks too much like the variable x.
• if we’re multiplying something, there are three ways we can show multiplication.
• 1. if something is being multiplied by a variable, we just stick them together, like the 3x. put the number before the variable. if it’s two variables, put them in alphabetical order, like ax.
• 2. we put the two numbers in parenthesis, like this: (3)(4)
• 3. we put a dot or an asterisk between the two numbers, like this: 4 * 3. however, you might accidentally mistake the dot for a decimal point, so it’s better to use the other two options.
• now, let’s go back to the equation.
• we learned in the previous lesson that in order to solve an equation, we need to find out what x equals.
• so we would need to get rid of the 3 in the 3x in order to only have x, right?
• we need to undo multiplication.
• now, let’s think about this for a second. when something was being added to x, we subtracted in order to make it only x. when something was being subtracted from x, we added in order to make it just x.
• so we could say that in order to undo an operation, you would need to do the opposite operation!
• addition and subtraction are opposites, and multiplication and division are opposites.
• so in order to undo x getting multiplied by 3, we would need to do x divided by 3, right?
• and then we would need to divide the other side by 3.
• now let’s talk about division.
• instead of using the ÷ symbol for division, we put it as a fraction! in a computer, it would be written like this: x/3
• let’s try to solve this equation now using concepts we learned in the first lesson and the previous part of this lesson.
• if we use division to undo multiplication, what would we use to undo division?
• that’s right, we would use multiplication!
• so we would multiply both sides by 3
• you could also think of it like simplifying a fraction.
• the final answer would be: x = 27
• now let’s go do some practice problems!
• let’s try to solve an equation now using concepts we learned in the first lesson and the previous part of this lesson.
• you've completed lesson 2!
• okay, so now we know how to solve equations with addition, subtraction, multiplication, and division. but what if the equation had two- or more- of those?
• well, in any equation, you need to undo things added or subtracted to the x first, and then things multiplied or divided by the x.
• it’s basically reverse order of operations.
• so let’s try that out on our example.
• first, we need to subtract 3 from both sides.
• and then we would divide both sides by 3.
• it's the same basic concept for all equations!
• now go try some practice problems on your own!
• okay, so now we know how to solve equations with addition, subtraction, multiplication,and division. but what if the equation had two- or more- of those?
• you've completed lesson 3!
• let’s start this lesson off with an example:
• but wait! is that a negative i see?
• if we divided both sides by 3, it would become -x = 2
• but that’s not x =
• so how would we get rid of the negative?
• well, two negatives make a positive, right?
• so if we divided both sides by -3…
• … it would become x = - 2
• now let’s try a harder example:
• as with every equation, we start by undoing the addition or subtraction to the x.
• now we need to multiply by negative 3 to undo division by negative 3
• you've completed lesson 4!
• like the last few lessons, we’re going to start this lesson off with an example as well!
• oh no! there are variables on both sides, but we only know how to solve equations with variables on one side!
• so we need to move one of the variables over to the other side. let’s go with moving 2x.
• if we wanted to get rid of addition or subtraction on one side, what would we do?
• we would add back or subtract away that amount!
• so we need to subtract 2x
• now both variables are on one side!
• now we need to subtract 2x from 3x. in order to do that, we just need to subtract their coefficients, or the numbers that they’re being multiplied by.
• 1 times anything won’t change it, so x = -2
• let’s do some more practice with adding variables together:
• you can think of that as 1x + 1x = 2
• 1 + 1 is 2, so that would be 2x = 2
• this is called simplifying an equation. we always want to do this before we start solving.
• remember, though, you can only simplify with variables that are the same! you wouldn’t be able to simplify 2x + 3y, because x and y are different!
• you also can’t simplify 2x + 1, because one of them has the variable x, and the other has no variable.
• however, you would want to simplify 2 + 2 or 3x + x
• now that you know all this, go use your knowledge to do some practice problems!
• you've completed lesson 5!
• 3x/3 + 2 = 2x - 3
• 3x/7 = x/7 * 2 + 7
• 7x/7 + 5 = 2x * 3 + 40
• you've completed lesson 6!
• we’re going to start this lesson off with…
• you guessed it…
• first, we could simplify the 3/3x like a fraction.
• the 3’s reduce, making the equation 3x = x
• now all we need to do is subtract x from both sides…
• and then divide by 2…
• now for another example!
• since there is only multiplication in 3x * 3, and multiplication is commutative, we can think of it like 3 * 3 * x, and only multiply the two 3’s.
• now all we need to do is subtract x…
• now another example! keep it up!
• first, we need to make sure only one side has a variable. since it’s negative 3x, we would need to add 3x in order to make it zero. anything plus or minus zero is itself, so it would only be 10 on the right side.
• now, just like we’ve done with other equations, we need to subtract 2 from both sides.
• now we need to divide both sides by 8.
• okay! that wasn’t too bad, right? now let’s do another slightly harder example!
• first, we would need to make sure that the variable is only on one side, so we would need to subtract x/3.
• now we just need to subtract 2x/3 and x/3 like we would any other fraction- the denominators stay the same, the numerators are added/subtracted.
• then we would need to multiply both sides by 3.
• but remember, the denominators have to be the same. if they aren’t, you would have to multiply top and bottom of one of the fractions to make the two denominators the same.
• let’s try to simplify an example with this.
• let’s make the denominator of 2x/3 equal to the denominator of x/6
• first we would multiply top and bottom by 2
• so the answer simplified is 5x/6
• now it’s time for some practice problems!
• in this lesson, we’re going to learn about the distributive property!
• basically, it states that a(b+c) = ax + ay or that a(b-c) = ab - ac
• a, b, and c representing real numbers. also, remember that having two variables right next to each other means that they are being multiplied together. having something in parenthesis directly next to something else also means that they’re being multiplied.
• let’s use the distributive property to solve an equation.
• a times b+c is ab+ac, so 3 times 2+x is 3*2+3x
• now it’s turned into an equation we can solve!
• now let’s do another example using the distributive property!
• a(b+c) is ab+ac, so 2(x-3) is 2x + 2 * -3
• let me give you a few other tips for using this property.
• if the equation is -(b + c), we can treat it as -1(b+c). -1 times any number makes it become its opposite (negative becomes positive, positive becomes negative), so it would become -b - c
• if the equation was -(b-c), it would be -b+c, with the c being positive because it was originally negative and then multiplied by a negative.
• now time to test your skills- by doing practice problems!
• 5 + 2( -7 + 2x) = 3
• -3(2 + 2x) = -48
• you've completed lesson 7!
• in this lesson, we’re going to learn about a special type of equation where the variables disappear. there are two possible outcomes for this.
• let’s start off with an equation we know how to solve:
• first, we subtract 3x from both sides to make the variable only on one side.
• but wait! the variable altogether disappeared!
• however, the equation created is true: 3 does equal 3
• this means that any real number will work. since you haven’t learned much about real and imaginary numbers yet, let’s just say that any number you know works.
• let’s test this out by plugging 2 into the x. you can also do this to check your other equations- plug in your solution to the variable.
• 9 does equal 9, so our solution is correct! you can also go check this with other real numbers.
• now let’s do another example that will give us a different type of answer!
• the variables disappeared, just like in the last equation!
• but this time, 4 does not equal 9, so there are no real number solutions.
• basically, none of the numbers you know so far will solve this equation.
• you can test this by plugging a bunch of numbers into the variable. none of them will make the equation correct.
• oh, and good news for you kids!
• this is the last lesson!
• we’re going to go do some practice problems with concepts from all the lessons now, and then you’re free! as a side note, write “no solution” or “all real solutions” if your answer is one of the “special” equations.
• have fun and good luck in your life!
• all real numbers
• x(3 + 4) = 3x + 4x
• 6x + 5 = 8 + 7(x - 8)
• you've completed all of the lessons!
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• 5x+3x+2=-3x+3x+10
• 2x/3-x/3=x/3-x/3+5
• Screen Shot 2017-06-29 at 3.53.05 PM
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### Images

• background scene - stage 1
• background scene - winter landscape
• background scene - laboratory
• background scene - SpaceBG_2DimStars
• background scene - SpaceBG_3
• background scene - grid
• background scene - bubble
• background scene - parchment card
• background scene - hexagon
• Ethan0 - 1
• Ethan0 - actor
• Back/skip - skip
• Back/skip - Back
• Ethan_greet - actor
• Ethan_greet - speaking
• Intro - Screen Shot 2017-06-22 at 4.41.13 PM
• Lesson1 - Screen Shot 2017-06-22 at 4.41.20 PM
• Lesson2 - Screen Shot 2017-06-26 at 8.24
• Lesson3 - Screen Shot 2017-06-26 at 9.03
• Lesson4 - Screen Shot 2017-06-28 at 3.26
• Lesson5 - Screen Shot 2017-06-28 at 3.27
• Example_01 - 3+x=8
• Example_01 - 3=3
• Example_01 - 3+2=3+2
• Example_01 - 5=5
• Example_01 - x+3-3=
• Example_01 - x=
• Example_01 - x=8-3
• Example_01 - x=5
• Example_01 - x-3=8
• Example_01 - x-3+3=
• Example_01 - x=8+3
• Example_01 - x=11
• Example_01 - ExampleF
• Red_circle - actor
• Here it is! - Screen Shot 2017-06-22 at 7.02.20 PM
• Arrow - actor
• Ethan_1 - 1
• Ethan_1 - actor
• Ethan_2 - 1
• Ethan_2 - actor
• Ethan_3 - 1
• Ethan_3 - actor
• Ethan_4 - 1
• Ethan_4 - actor
• Ethan_5 - 1
• Ethan_5 - actor
• Ethan_6 - 1
• Ethan_6 - actor
• Ethan_7 - 1
• Ethan_7 - actor
• Ethan_8 - 1
• Ethan_8 - actor
• Continue_1 - Screen Shot 2017-06-24 at 3.16.09 PM
• Replay_1 - Screen Shot 2017-06-24 at 3.16.15 PM
• Continue_2 - Screen Shot 2017-06-24 at 3.16.09 PM
• Replay_2 - Screen Shot 2017-06-24 at 3.16.15 PM
• Example_23 - 3x=9
• Example_23 - x=3
• Example_23 - x/3=9
• Example_23 - x=27
• Example_23 - Ex1
• Example_23 - 3x/3
• Example_23 - x=9/3
• Example_23 - 3 * x/3 = 9 * 3
• Example_23 - 3x+3=9
• Example_23 - 3x+3-3=9-3
• Example_23 - 3x=6
• Example_23 - x=2
• Example_23 - 3x/3=6/3
• Replay_3 - Screen Shot 2017-06-24 at 3.16.15 PM
• Continue_3 - Screen Shot 2017-06-24 at 3.16.09 PM
• Example_45 - -3x=6
• Example_45 - -3x/-3=6/-3
• Example_45 - x=-2
• Example_45 - x/-3+1=2
• Example_45 - x/-3+1-1=2-1
• Example_45 - x/-3=1
• Example_45 - x/-3*-3=1*-3
• Example_45 - x=-3
• Example_45 - Screen Shot 2017-06-28 at 6.04
• Example_45 - 3x-2x=2x-2x-2
• Example_45 - 3x-2x=-2
• Example_45 - 1x=-2
• Example_45 - x=-21
• Example_45 - x+x=2
• Example_45 - 1x+1x=2
• Example_45 - 2x=2
• Replay_4 - Screen Shot 2017-06-24 at 3.16.15 PM
• Continue_4 - Screen Shot 2017-06-24 at 3.16.09 PM
• Continue_5 - Screen Shot 2017-06-24 at 3.16.09 PM
• Replay_5 - Screen Shot 2017-06-24 at 3.16.15 PM
• Continue_6 - Screen Shot 2017-06-24 at 3.16.09 PM
• Replay_6 - Screen Shot 2017-06-24 at 3.16.15 PM
• Lesson6 - Screen Shot 2017-06-28 at 8.06.43 PM
• Example_66 - 3x=3x/3
• Example_66 - 3x=x
• Example_66 - 3x-x=x-x
• Example_66 - 2x=0
• Example_66 - 2x/2=0/2
• Example_66 - x=0
• Example_66 - 16+x=3*3x
• Example_66 - 16+x=3*3*x
• Example_66 - 16+x=9x
• Example_66 - 16+x-x=9x-x
• Example_66 - 16=8x
• Example_66 - 16/8=8x/8
• Example_66 - 2=x
• Example_66 - 5x+2=-3x+10
• Example_66 - 5x+3x+2=-3x+3x+10
• Example_66 - 8x+2=10
• Example_66 - 8x+2-2=10-2
• Example_66 - 8x=8
• Example_66 - 8x/8=8/8
• Example_66 - x=1
• Example_66 - 2x/3=x/3+5
• Example_66 - 2x/3-x/3=x/3-x/3+5
• Example_66 - 2x/3-x/3=5
• Example_66 - x/3=5
• Example_66 - x/3*3=5*3
• Example_66 - x=15
• Example_66 - x/6+2x/3
• Example_66 - 2x*2/3*2
• Example_66 - x/6+4x/6
• Example_66 - 5x/6
• Example_7 - 3(2+x)=9
• Example_7 - 3*2+3x=5
• Example_7 - 6+3x=9
• Example_7 - 6-6+3x=9-6+3x
• Example_7 - 3x=3
• Example_7 - 3x/3=3/3
• Example_7 - x=1
• Example_7 - 2(x-3)=8
• Example_7 - 2x-2*3=8
• Example_7 - 2x-6=8
• Example_7 - 2x-6+6=8+6
• Example_7 - 2x=14
• Example_7 - 2x/2=14/2
• Example_7 - x=7
• Lesson7 - Screen Shot 2017-06-29 at 3.53.05 PM
• Continue_7 - Screen Shot 2017-06-24 at 3.16.09 PM
• Replay_7 - Screen Shot 2017-06-24 at 3.16.15 PM
• Lesson8 - Screen Shot 2017-06-29 at 4.24.33 PM
• Continue_8 - Screen Shot 2017-06-24 at 3.16.09 PM
• Replay_8 - Screen Shot 2017-06-24 at 3.16.15 PM
• Example8 - 3x+3=3x+3
• Example8 - 3x-3x+3=3x-3x+3
• Example8 - 3=3
• Example8 - 3(2)+3=3(2)+3
• Example8 - 6+3=6+3
• Example8 - 9=9
• Example8 - 3x+4=3x+9
• Example8 - 3x-3x+4=3x-3x+9
• Example8 - 4+9

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