Solving One-Step Equations with Negatives (Multiplication and Division) | Math with Mr. J

[Music] welcome to math with Mr J in this video I'm going to cover how to solve one-step multiplication and division equations with negatives now when we solve one-step equations with negatives we solve them the same way we solve one-step equations that have only positives we want to isolate the variable which means get it by itself and we do this by using the inv verse operation which means the opposite operation basically we want to undo whatever is being done to the variable that way the variable is by itself on one side of the equation and again we do this by using the inverse or opposite operation just remember whatever is done to one side of the equation it must be done to the other in order to keep everything balanced and equal let's jump into number one where we have -6x = -36 now we have a number next to a variable that means we are multiplying this is -6 * X = -36 so whenever you see a number next to a variable that is representing multiplication so something to keep in mind now we need to isolate that variable of X we need to figure out what x equals since X is being multiplied by -6 we need to undo that multiplication by using the inverse operation so the opposite operation the opposite of multiplication is division so let's divide the left side of the equation by -6 whatever we do to one side of the equation we must do to the other in order to keep it balanced and equal so let's divide the right side by -6 as well now let's take a look at the left side of the equation we are multiplying by -6 and dividing by -6 so these -6 cancel out they equal a positive 1 because we have -6 / -6 a negative / a negative equals a positive so we end up with a positive 1 this gives us 1 X which is just X so X is now isolated it's by itself x equals and then on the right side of the equation -36 / -6 equal a postive 6 because again a negative / a negative equals a positive so this is our solution x = 6 now we can always check a solution by plugging it into the original equation so let's plug 6 in for x and see if this works so we have ne6 * a POS 6 = -36 a * a positive equals a negative so -6 * a POS 6 does equal 36 we have the correct solution x = 6 let's move move on to number two where we have 77 = -7 e so we need to isolate that variable of e e is being multiplied by -7 we need to undo that multiplication by using the inverse operation the inverse of multiplication is division so let's divide the right side by -7 whatever we do to one side of the equation we must do to the other so so let's divide the left side by -7 as well now taking a look at the right side of the equation we are multiplying by -7 and dividing by -7 so these -7 cancel out they equal 1 we have -7 / -7 that gives us 1 E which is just e our variable is now isolated it's by itself E equals and then on the left side of the equation we have 77 / -7 so a positive / a negative that's going to equal a netive so we get 11 eal1 and we can reite this with the variable coming first so E equals -11 let's check that Solution by plugging -11 in for E so we have 77 = -7 * 11 we have a Nega * a Nega -7 * -1 a * a Nega equals a positive so -7 * -11 does equal 77 a positive 77 we have the correct solution eal1 there's how we solve one-step multiplication equations with negatives let's move on to division here are our examples of one-step division equations with negatives let's jump into number one where we have h / 5 = -9 now we need to isolate that variable of H we need to figure out what H equals since H is being divided divided 5 we need to undo that division by using the inverse operation so the opposite operation the opposite of division is multiplication so let's multiply the left side of the equation by five now whatever we do to one side of the equation we must do to the other in order to keep it balanced and equal let's multiply the right side of the equation by five as well now let's take a look at the left side of the equation we are dividing by five and multiplying by five so these fives cancel out they equal one because when we multiply h / 5 by 5 we end up with 5H over 5 we have 5 / 5 which gives us that one and then we have the H we end up with 1 h which is just H our variable is now isolated H is by itself so H equals and then on the right side of the equation we have -9 * 5 we have a NE * a positive which equals a negative so this equals 45 H equal -45 that's our solution now we can always check a solution by plugging it into the original equation so let's plug -45 in for H so we have -45 / 5 equal 99 we have a negative ided by a positive -45 / a postive 5 a negative / a positive equals a negative -45 / 5 does equal -9 so we have the correct solution H equal -45 let's move on to number two where we have -3 = k / -8 we need to isolate that variable of K since K is being divided by -8 we need to undo that division by using the inverse operation the inverse of division is multiplication so let's multiply the right side by 8 whatever we do to one side we must do to the other so let's multiply the left side by8 as well now as far as the right side of the equation we are dividing by8 and multiplying by8 so these 8s cancel each other out they equal 1 we have8 / 8 a NE divided by a negative is a positive so that gives us positive 1 so we have 1 K which is just K our variable is now isolated k equals and then on the left side of the equation we have 8 * -3 a NE * a negative equals a positive so this gives us a positive 24 k equal 24 and we can rewrite this with the variable coming first K = 24 that's our solution let's check that Solution by plugging it into the original equation so let's plug in 24 for K so we have -3 equal 24 /8 we have a positive / a negative that's going to equal a negative 24 / -8 does equal -3 so we have the correct solution k equal 24 so there you have it there's how you solve onestep multiplication and division equations with negatives I hope that helped thanks so much for watching until next time peace