[Music] welcome to math with Mr J in this video I'm going to go through an introduction to solving equations with variables on both sides now when we solve equations with variables on both sides we want to look to get the variable on one side of the equation so we just want the variable on one side then we can look to solve let's jump into our examples and see what this looks like starting with number one where we have 5x - 4 = 2x + 11 so we need to figure out what x equals the first thing that we need to do we need to get the variable so it's just on one side of the equation now we can do this either way we can get the variable on the left or on the right either way 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 2x for number one so let's get the variable on the left side only here that means we need to undo or get rid of the 2x on the right side that's a positive 2x so the inverse operation would be to subtract 2x so let's subtract 2x from the right side of the equation whatever we do to one side of the equation we must do to the other so subtract 2x from the left side as well now on the right side of the equation we have positive 2X and then minus 2x so these 2 X's cancel each other out and we are left with 11 on the right side of the equation and then on the left side of the equation we have 5x - 2x so we can subtract those like terms that's going to give us 3x and then we can bring down the rest of the left side here so - 4 so now we have 3x - 4 = 11 and that variable is on one side we have it on the left side only now and now we can solve so we need to isolate that variable of X and remember we do that by using inverse operations 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 four to the left side of the equation whatever we do to one side we must do to the other so add four to the right side as well now on the left side we are subtracting four and adding four so these fours cancel each other out we now have 3x equals and then on the right side 11 + 4 gives us 15 so we have 3x = 15 3 * x = 15 so we need to isolate that variable of X so what's the inverse operation of multiplication well division so divide the left side by three whatever we do to one side of the equation we must do to the other so divide the right side by three as well now on the left side we are multiplying by three and dividing by three so these threes cancel each other out X is now isolated so we have x equals and then on the right side 15 / 3 gives us 5 so x equals 5 that's our solution now let's check that Solution by plugging it in for x and seeing if it works so let's come to the side here we have 5 * 5 - 4 = 2 * 5 + 11 let's work through the left side first so we have 5 * 5 which is 25 25 - 4 gives us 21 now on the right side we have 2 * 5 which is 10 and 10 + 11 is 21 as well so both sides equal 21 we are correct x = 5 let's move on to number two where we have 3 y + 8 = 10 y - 6 so we have that variable of Y on both both sides we need to get the variable on one side and then we can look to solve we need to decide which side of the equation we want the variable on like I mentioned earlier either way 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 we have a three in front of the variable and a 10 in front of the variable three is smaller in value so let's get rid of the 3 y now that's a positive 3 y so the inverse operation subtract so let's subtract 3 y from the left side whatever we do to one side we must do to the other so subtract 3 y from the right side as well on the left side of the equation we have a positive 3 y - 3 y so these three y's cancel each other out we now have 8 equals and then on the right side we can subtract those like terms so 10 y - 3 y gives us 7 Y and then we can bring down the rest of the right side so Min - 6 and now we have 8 on the left side of the equation equals 7 y - 6 which is on the right side of the equation so we need to isolate that variable of Y so we need to undo the subtraction action first the inverse operation is addition so add six to the right side of the equation that means we need to add six to the left side as well now on the right side of the equation we are subtracting six and adding six so these sixes cancel each other out and now we have 7 y equals and then on the left side 8 + 6 gives us 14 so now we have 7 y on the right side of the equation equals 14 on the left side so we have 7 * y = 14 we need the inverse operation the inverse operation of multiplication is division so divide the right side by seven that means we need to divide the left side by seven as well now on the right side we are multiplying by seven and dividing by seven so these these sevens cancel each other out Y is now isolated so we have y equals and then on the left side 14 / 7 gives us 2 so Y = 2 that's our solution now let's check that by plugging it in for y and seeing if it works so we have 3 * 2 + 8 = 10 * 2 - 6 let's start with the left side so we have 3 * 2 start with multiplication that gives us 6 and then we have 6 + 8 which is 14 now for the right side so let's start with multiplication 10 * 2 gives us 20 and then we have 20 - 6 which is 14 so we get 14 on both sides we are correct Y = 2 so there you have it there's an intro to solving equations with variables on both sides I hope that helped thanks so much for watching until next time peace