How to Solve One-Step Equations with Negatives | Solving Algebraic Equations | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover how to solve one-step equations with negatives I'll go through one step addition subtraction multiplication and division equations we'll start with addition 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 inverse 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 let's jump into number one where we have y plus 11 equals negative 20. now we need to isolate that variable of Y we need to figure out what y equals since 11 is being added 2y we need to undo that addition by using the inverse operation so the opposite operation the opposite of addition is subtraction so let's subtract 11 from the left side of the equation now 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 subtract 11 from the right side as well now if we take a look at the left side of the equation we are adding 11 and subtracting 11. so these 11s cancel each other out they equal zero so Y is now isolated it's by itself y equals now on the right side of the equation we have negative 20 minus 11. so we're starting with negative 20 and subtracting 11. so we are decreasing in value by 11. we end up with negative 31 so y equals negative 31. now one thing I do want to mention it's always an option to come to the side in order to figure out a problem for example negative 20 minus 11 we did vertically you can come to the side and rewrite this horizontally if you prefer now when we subtract we can add the opposite so let's add the opposite here add the opposite so negative 20 plus negative 11 gives us that negative 31. so again you can always come to the side to show work or set up a problem differently so something to keep in mind so our solution for number one is negative 31. we can always check a solution by plugging it into the original equation so let's plug negative 31 in for y and see if this works negative 31 plus 11 equals negative 20. so we're starting at negative 31 and adding 11. so we are increasing in value by 11 negative 31 plus 11 does equal negative 20 so we have the correct solution y equals negative 31. let's move on to number two where we have negative 12 equals B plus negative 7. we need to isolate that variable of B negative 7 is being added to B so we need to undo that addition by using the inverse operation let's subtract negative seven from the right side whatever we do to one side of the equation we must do to the other so let's subtract negative seven from the left side as well now if we take a look at the right side of the equation we are adding a negative seven and subtracting a negative seven these negative sevens are going to cancel out and equal zero but it's kind of difficult to think through when we are subtracting a negative when we subtract a negative we actually increase in value and remember we can add the opposite that's going to make this simpler to think through and see how the variable ends up isolated so let's add the opposite add and then the opposite of negative seven is positive seven so whenever we subtract a negative we can add a positive so now we have a negative seven and a positive 7. these sevens cancel out they equal zero so the variable is now isolated B equals and then on the left side we have negative 12 minus negative 7. let's add the opposite add the opposite negative 12 plus a positive 7 equals negative 5. so b equals negative five we can rewrite this with the variable coming first and remember we can always come to the side in order to show work or set up a problem differently for example let's do negative 12 minus negative seven off to the side and set it up horizontally let's add the opposite so add the opposite negative 12 plus a positive 7 gives us negative five now let's check that solution of negative five and plug it in for B so negative 12 equals negative five Plus negative seven negative five plus negative seven does equal negative 12 so we have the correct solution b equals negative five there's how we solve One Step addition equations with negatives let's move on to subtraction here are our examples of one step subtraction equations with negatives let's jump into number one where we have J minus 14 equals negative 10. we need to isolate that variable of J we need to figure out what J equals since 14 is being subtracted from J we need to undo that subtraction by using the inverse operation so the opposite operation the opposite of subtraction is addition so let's add 14 to the left side of the equation now whatever we do to one side of the equation we must do to the other so let's add 14 to the right side as well now on the left side we are subtracting 14 and adding 14. so these 14s cancel out they equal zero the variable is now isolated J Is Now by itself so we have J equals and then on the right side of the equation we have negative 10 plus 14. we are starting at negative 10 and increasing in value by 14 so we end up with positive 4 J equals 4. now one thing I do want to mention we always have the option to come to the side in order to show work or set up a problem differently for example negative 10 plus 14 we solved vertically so up and down if you prefer to work through that horizontally you can always rewrite the problem off to the side so negative 10 plus 14 that equals four so you always have that option now J equals four that's our solution we can always check a solution and make sure it works by plugging it into the original equation so let's plug 4 in for J and see if this works so 4 minus 14 equals negative 10. 4 minus 14 does equal negative 10 so we have the correct solution J equals four let's move on to number two where we have 18 equals g minus negative three we need to isolate that variable of G negative three is being subtracted from G we need to undo that subtraction by using the inverse operation the inverse of subtraction is addition so let's add negative 3 to the right side of the equation whatever we do to one side we must do to the other so let's add negative three to the left side as well let's take a look at the right side of the equation now when we subtract a negative we are actually increasing in value so we are increasing G's value by three so by adding negative 3 to that side of the equation these cancel out and equal zero so our variable of G is now isolated so G equals and then on the left side of the equation 18 plus negative 3 equals 15. so g equals 15 and we can rewrite that with the variable coming first now if we look back up at the right side of the equation that can be a little confusing to think through because it looks like we have negative 3 plus negative 3 which would equal negative six not that zero which isolated our variable but keep in mind when we subtract a negative we increase in value so G is increasing in value by three by adding a negative 3 to that side of the equation we are canceling that increase out to equal zero and our variable was isolated here is an easier way to think about it whenever we subtract a negative we can think of this as adding a positive and remember when subtracting we can always add the opposite so this works out we can actually rewrite this as 18 equals g e plus three G plus a positive 3 because again we can add the opposite so add and then the opposite of negative 3 is positive three so you can always rewrite the equation if you're subtracting a negative to add a positive let's go through the Rewritten equation and see if we still get 15. we need to isolate G three is being added to G so let's undo that addition by using the inverse operation which is subtraction let's subtract 3 from the right side of the equation whatever we do to one side we must do to the other so subtract 3 from the left side as well on the right side we are adding three and subtracting three so these threes cancel out G is now isolated so G equals and then on the left side 18 minus 3 that equals fifteen so g equals 15 that way as well and I do want to mention one more time that we can always come to the side in order to show work or set up a problem differently for example let's do 18 plus negative 3 horizontally so side to side eighteen plus negative 3 18 plus negative 3 equals fifteen let's check that solution of 15 by plugging 15 in for G in the original equation and see if this works so we have 18 equals 15 minus negative 3. since we are subtracting a negative we are increasing in value 15 minus negative 3 does equal 18 and we can always add the opposite so add and then the opposite of negative 3 is positive 3. so 15 plus positive 3 gives us 18 as well we have the correct solution g equals 15. so there's how we solve One Step subtraction equations let's move on to multiplication so here are our examples of one step multiplication equations with negatives let's jump into number one where we have negative six x equals negative 36. now we have a number next to a variable that means we are multiplying this is negative 6 times x equals negative 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 negative 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 negative six 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 negative six as well now let's take a look at the left side of the equation we are multiplying by negative six and dividing by negative six so these negative sixes cancel out they equal a positive one because we have negative six divided by negative six a negative divided by a negative equals a positive so we end up with a positive one this gives us One 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 negative 36 divided by negative six equals a positive six because again a negative divided by a negative equals a positive so this is our solution x equals six now we can always check a solution by plugging it into the original equation so let's plug six in for x and see if this works so we have negative six times a positive 6 equals negative 36. a negative times a positive equals a negative so negative 6 times a positive 6 does equal negative 36. we have the correct solution x equals six let's move on to number two where we have 77 equals negative seven e so we need to isolate that variable of e e is being multiplied by negative seven 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 negative seven whatever we do to one side of the equation we must do to the other so let's divide the left side by negative seven as well now taking a look at the right side of the equation we are multiplying by negative seven and dividing by negative seven so these negative sevens cancel out they equal one we have negative seven divided by negative seven that gives us one 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 divided by negative seven so a positive divided by a negative that's going to equal a negative so we get Negative eleven E equals negative eleven and we can rewrite this with the variable coming first so E equals negative 11. let's check that Solution by plugging negative 11 in for E so we have 77 equals negative seven times negative eleven we have a negative times a negative negative seven times negative 11 a negative times a negative equals a positive so negative seven times negative 11 does equal 77 a positive 77. we have the correct solution E equals negative 11. 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 divided by 5 equals negative nine now we need to isolate that variable of H we need to figure out what H equals since H is being divided by five 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 5. 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 5 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 divided by five by five we end up with five H over five we have five divided by five which gives us that one and then we have the H we end up with one 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 negative nine times five we have a negative times a positive which equals a negative so this equals negative 45. H equals negative 45 that's our solution now we can always check a solution by plugging it into the original equation so let's plug negative 45 in 4H so we have negative 45 divided by five equals negative nine we have a negative divided by a positive negative 45 divided by a positive five a negative divided by a positive equals a negative negative 45 divided by 5 does equal negative nine so we have the correct solution H equals negative 45. let's move on to number two where we have negative three equals K divided by negative eight we need to isolate that variable of K since K is being divided by negative eight 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 negative eight whatever we do to one side we must do to the other so let's multiply the left side by negative eight as well now as far as the right side of the equation we are dividing by negative eight and multiplying by negative eight so these negative eights cancel each other out they equal one we have negative eight divided by negative eight a negative divided by a negative is a positive so that gives us positive one so we have one k which is just K our variable is now isolated k equals and then on the left side of the equation we have negative eight times negative three a negative times a negative equals a positive so this gives us a positive twenty four k equals 24 and we can rewrite this with the variable coming first k equals 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 negative 3 equals 24 divided by negative eight we have a positive divided by a negative that's going to equal a negative 24 divided by negative eight does equal negative three so we have the correct solution k equals 24. so there you have it there's how you solve one-step equations with negatives I hope that helped thanks so much for watching until next time peace