How to Solve One-Step Equations | An Introductory Guide | Algebra

[Music] welcome to math with Mr J in this video I'm going to go through an introduction to solving one-step equations we will start with addition and subtraction equations and then we will move on to multiplication and division equations now when we solve one-step equations we want to look to isolate the variable which just means to get the variable by itself we do that by using inverse operations and we can think of an inverse operation as the opposite operation basically we use an inverse operation to undo another operation and this will isolate the variable when we solve equations and always remember whatever we do to one side of the equation we must do to the other side of the equation this keeps everything balanced and equivalent let's jump into our addition and subtraction example examples starting with number one where we have x - 9 = 28 so we need to solve this equation we need to figure out what x equals so what - 9 equal 28 now for this example we may be able to figure it out using mental math but it's going to be helpful to go through the process of isolating the variable that way we're prepared for more difficult or more complex equations now we are subtracting 9 from X we need to undo that subtraction so to speak by using the inverse operation what's the inverse or opposite of subtraction well addition so we need to add 9 to the left side of the equation now remember whatever we do to one side of an equation we must do to the other in order to keep everything balanced and equivalent so we need to add nine to the right side as well now looking at the left side of the equation we are subtracting nine and adding nine so these nines cancel each other out and our variable X is now isolated so x equals and then on the right side of the equation we have 28 + 9 that gives us 37 so x equal 37 that's the solution of this equation now one last thing we can do we can always check to see if we are correct all we need to do is plug in what we got and see if it works so for example plug in 37 for X so let's go to the side plug in 37 for X so 37 - 9 = 28 37 - 9 is 28 so we are correct x equal = 37 let's move on to number two where we have a + 14 = 33 so what + 14 equal 33 so what's the inverse operation what's the opposite of addition well subtraction so let's subtract 14 from the left side of the equation whatever we do to one side we must do to the other so let's subtract 14 from the the right side as well on the left side of the equation we are adding 14 and subtracting 14 so these 14s cancel each other out a our variable is now isolated so a equals and then on the right side of the equation 33 - 14 gives us 19 so a equals 19 and that's our solution but let's check it by plugging 19 in for a and see if that works so 19 + 14 equal 33 19 + 14 is 33 so we are correct a equal 19 moving on to number three we have 75 = W + 31 now for number three the variable is on the right side of the equation so a little bit of a different look here but we use the same exact process so this doesn't change anything so we have what + 31 equals 75 we are adding 31 here so the inverse operation the opposite of addition is subtraction so let's subtract 31 from the right side of the equation whatever we do to one side we must do to the other so so subtract 31 from the left side as well now on the right side of the equation we are adding 31 and subtracting 31 so these 31s cancel each other out W is now isolated so we have W equals and then on the left side of the equation 75 - 31 = 44 so w equal 44 that's our solution now let's check that by plugging 44 in for w so 75 equal 44 + 31 44 + 31 is 75 so we are correct W equal 44 and then lastly number four we have 59 = M - 6 so we are subtracting 6 from M here we need the inverse operation the opposite of subtraction that's addition so let's add six to the right side of the equation whatever we do to one side we must do to the other so add six to the left side as well on the right side of the equation we are subtracting six and adding six so those sixes cancel each other out m is now isolated so we have m equals and then on the left side of the equation 59 + 6 gives us 65 so m equals 65 that's our solution now let's check it by plugging 65 in 4 M so we have 59 equal 65 - 6 65 - 6 is 59 so we are correct M = 65 so there's our addition and subtraction section let's move on to multiplication and division now let's take a look at our multiplication and division examples and jump into number one where we have y / 6 = 8 remember when we have something in fractional form like that we divide now we are dividing y by 6 so we need to undo that division so to speak by using the inverse operation what's the inverse or opposite of division well multiplication so let's multiply the left side of the equation by six whatever we do to one side of the equation we must do to the other side of the equation in order to keep everything balanced and equivalent so let's multiply the right side of the equation by six as well well now on the left side of the equation we are dividing by six and multiplying by six so these sixes cancel each other out y our variable is now isolated so y equals and then on the right side of the equation we have 8 * 6 which is 48 so y equals 48 that's our solution and one last thing we can do here we can always check to see if we are correct all we need to do is plug in what we got and see if it works so for example plug in 48 for y so off to the side let's plug in 48 for y so 48 ided 6 equal 8 48 / 6 does equal 8 so we are correct y = 48 let's move on to number two where we have 11x equals 77 and remember when we have a number next to a variable that's multiplication so this is 11 * what equal 77 so we need the inverse operation the opposite operation here so what's the opposite of multiplication well division so let's divide the left side of the equation by 11 whatever we do to one side we must do to the other so divide the right side of the equation by 11 as well on the left side of the equation we are multiplying by 11 and dividing by 11 so these 11s cancel each other out X is now isolated so x equals and then on the right side of the equation we have 77 / 11 that gives us 7 so x equal 7 so that's our solution now now let's check that by plugging 7 in 4X so 11 * 7 equal 77 11 * 7 is 77 so we are correct x = 7 let's move on to number three where we have 25 = C divided 5 now for numbers three and four the variable is on the right side of the the equation so a little bit of a different look here but we use the same exact process so this doesn't change anything so for number three we have what divided 5 equals 25 we are dividing C by 5 what's the inverse operation the opposite of division well multiplication so let's multiply the right side by five whatever we do to one side we must do to the other so multiply the left side by five as well on the right side of the equation we are dividing by five and multiplying by five these fives cancel each other out c is now isolated so C equals and then on the left side of the equation 5 * 25 gives us25 so C equals 125 that's our solution now let's check it by plugging 125 in for C so 25 equals 125 / 5 125 ID 5 is 25 so we are correct C equals 125 lastly let's move on to number four where we have 80 = 4 W so 4 * what equals 80 so what's the inverse operation here what's the opposite of multiplication well division so let's divide the right side of the equation by four whatever we do to one side we must do to the other so divide the left side by four as well on the right side of the equation we are multiplying by four and dividing by four so those fours cancel each other out W is now isolated so we have W equals and then on the left side we have 80 / 4 which is 20 so w equals 20 that's our solution now let's check it by plugging 20 in for w so 80 equal 4 * 20 4 * 20 is 80 so we are correct W equal 20 so there you have it there's an intro to solving one-step equations I hope that helped thanks so much for watching until next time peace