[Music] welcome to math with Mr J in this video I'm going to cover how to solve multistep equations we will go through two examples and for these examples we may Use the distributive property we may combine like terms and we may have variables on both sides these are all things we need to be aware of when solving equations let's jump into our first example where we have x + 5 and then in parentheses 3x - 4 and parentheses equals 12x + 4 so looking at this equation let's work through this step by step we will start by using the distributive property then we will combine like terms and then since we have variables on both sides we will get the variable to one side then we will look to solve we will look to isolate the variable now those steps are the top of the screen and I have question marks by them because not all equations are the same so we can ask ourselves these steps as we look to solve equations can I distribute anything using the distributive property can I combine like terms are there variables on both sides and then lastly we need to solve which doesn't have a question mark because it doesn't matter what type of equation we have we will look to solve we will look to isolate the variable now let's start with the first thing that we're going to do and that is to look for an opportunity to Use the distributive property to remove any parentheses so do we have any parentheses that we can remove yes we can use the distributive property to remove the parentheses around 3x - 4 we need to distribute five and that's a positive 5 to 3x and -4 so if we distribute 5 to 3x we have 5 * 3x that gives us 15x and then Distributing 5 to -4 so 5 * -4 that gives us -20 so minus 20 and then we can bring down the rest of the equation so x + 15x - 20 = 12x + 4 now that we removed the parentheses we can look for any like terms that we can combine are there any like terms yes we have X and 15x we can combine those like terms on the left side of the equation so combining X and 15x we can think of this as x + 15x that gives us 16 16 x and then bring down the rest of the equation so - 20 = 12x plus 4 so we used the distributive property we combined like terms and now since we have variables on both sides we need to get the variable to one side of the equation now either side will work but my suggestion look to avoid negatives as far as the variable goes and we can do that by getting rid of the one with the coefficient that is smaller in value so the number in front of the variable that is smaller in value that's going to be 12x so let's get rid of 12x from the right side of the equation now that's a positive 12x so the inverse operation is going to be subtraction so let's subtract 12x from the right side of the equation whatever we do to one side we must do to the other so subtract 12x from the left side as well now on the right side of the equation these 12 X's cancel each other out so we are left with four and that's a positive 4 equals and then on the left we can do 16x - 12x so subtract those like terms that gives us 4X bring down the rest of the the equation so now we have 4x - 20 = 4 now that we have the variable on one side of the equation we can look to solve we can look to isolate the variable we're going to use inverse operations in order to do so and we're going to go in the reverse order of operations so we need to undo the subtraction first what's the inverse operation of subtraction well addition so let's add 20 to the left side of the equation whatever we do to one side we must do to the other so add 20 to the right side as well now on the left side we are subtracting 20 and adding 20 so these 20s cancel each other out we now have 4X equals and then on the right side we have 4 + 20 that gives us 24 so now we have 4X = 24 4 * x = 24 so we need to undo that multiplication what's the inverse operation of multiplication well division so let's divide the left side by four that means we need to divide the right side by four as well now on the left side we are multiplying by four and dividing by four so these fours cancel each other out X is now isolated and then on the right side we have 24 / 4 that gives us 6 so xals 6 that's our solution now we can check that by plugging it in for x and seeing if this works so let's do that off to the side so let's plug in six 4 x here now we need to work through both sides of the equation and see if they are equal if they are then we have the correct solution let's start with the left side of the equation and we will start in the parentheses we have 3 * 6 - 4 3 * 6 is 18 - 4 gives us 14 and then we can bring down the rest of the equation and now we have 6 + 5 * 14 so we need to do multiplication next 5 * 14 gives us 70 and then we end with 6 + 70 that gives us 76 now let's do the right side and see if we get 76 so we have 12 * 6 + 4 let's start with the multiplication so 12 * 6 is 72 and then we have 72 + 4 which is 76 both sides equal 76 so we are correct x equal 6 so there's how to work through a multi-step equation involving the distributive property combining like terms and variables on both sides let's take a look at another example of a multi-step equation let's jump into to our next example where we have -9 and then in parentheses M - 2 and parentheses + 7 m = -10 so looking at this equation let's work through this step by step we will start by looking to see if we need to use the distributive property then we can look to see if we can combine any like terms and then if we end up having variables on both sides of the equation we will need to take care of that for this example we will not have variables on both sides and then lastly we can look to solve we can look to isolate the variable now the first thing that we're going to do is look for any opportunity to Use the distributive property to remove any parentheses so do we have any parentheses that we can remove can we use the distributive property yes we can use the distributive property to remove the parentheses around M - 2 we need to distribute -9 to M and -2 keep in mind use the sign that is in front so that is -9 being distributed -9 distributed to the m so -9 * m gives us 9 M and then -9 being distributed to -2 so -9 * -2 gives us a positive 18 remember a NE * a negative equals a positive so we have plus 18 and then we can bring down the rest of the equation so + 7 m equal10 now that we removed the parentheses we can look for any like terms that we can combine are there any like terms yes -9 M and 7M combining -9 M and 7M so we can think of this as -9 m + 7 m that gives us2 M and then bring down the rest of the equation so + 18 = -10 and now we have --2m + 18 = -10 now we can look to solve we can can look to isolate that variable we don't have variables on both sides or anything else like that that we need to take care of so we are good to go again we need to isolate that variable of M and we're going to do this by using the inverse operations and go in the reverse order of operations so we need to undo the addition first the inverse operation of addition is subtraction so let's subtract 18 from the left side of the equation whatever we do to one side we must do to the other so subtract 18 from the right side as well on the left side of the equation we are adding 18 and subtracting 18 so these 18s cancel each other out and now we have -2 m equals and then on the right side we have -10 - 18 that gives us 28 so now we have -2 M = -28 so -2 * m = -28 so we need to undo that multiplication what's the inverse operation of multiplication well division so divide the left side by -2 that means we need to divide the right side by -2 as well on the left side we are multiplying by -2 and dividing by -2 so these -2 cancel each other out m is now isolated so we have m equals and then on the right side we have -28 / -2 so a negative ided by a negative that's going to give us a positive so this gives us positive 14 and that's our solution m equal 14 now let's check that Solution by plugging it in for M and seeing if this works so let's come to the side here -9 then we have 14 - 2 + 7 * 14 = -10 let's start with parentheses here 14 minus 2 gives us 12 bring everything else down here then we can do multiplication so we have -9 * 12 which gives us18 + bring everything down and we will go one step at a time here so we have more multiplication 7 * 14 gives us 98 so we have -18 plus a positive 98 this gives us10 so 14 is correct that's our solution m equals 14 so there you have it there's two examples of how to solve a multi-step equation I hope that helped thanks so much for watching until next time peace