welcome to math with mr. J in this video I'm going to cover how to solve two-step equations we have for example problems on your screen there that we're going to go through together in order to get this down now remember when we have an equation with a variable our goal is to isolate that variable or get it by itself in order to solve and we also need to remember whatever we do to one side we must do to the other side of the equation we have to keep it balanced so let's jump right into the number one and solve some two-step equations so for number one we have 2x minus 6 equals 10 so again we want to isolate that X get it by itself so I like to think of it as we need to reverse the order or undo this side of the equation so we get that X by itself and we're going to use the reverse order of operations in order to do so so we have 2 times that X and then we subtract a 6 so reverse order of operations this subtraction of 6 needs to come first so how do we get rid of that 6 from the left side well we can add 6 that will cancel those sixes out or give us a 0 so remember whatever we do to one side we have to do to the other so if we add 6 to the left we need to add 6 to the right a negative 6 or minus 6 plus 6 gives us that 0 and 10 plus 6 is 16 so on the left side we're left with 2 times X or 2x so we don't have the variable completely isolated yet but we're almost there so we have 2 times X so how do we get rid of that 2 we need to either make it a 0 or a 1 so the opposite of multiplying by 2 would be dividing by two that would give us one X on that side which is the same as just X so let's divide both sides by two and that leaves us with x equals 16 divided by 2 is 8 now let's plug in that 8 into the original original equation and see if we get the correct answer so 2 times 8 minus 6 equals 10 it's always a good idea to see if that answer works out 2 times 8 is 16 minus 6 does give us that 10 so we have the correct answer x equals 8 so for number two we have R divided by 5 plus 8 equals 11 so we need to get that R by itself so let's do the reverse order of operations to undo the left side of the equation so let's get rid of that 8 first so we have plus 8 so the opposite let's subtract 8 from both sides to begin to isolate the R so a positive 8 and a negative 8 there minus 8 gives us zero and 11 minus 8 gives us 3 so on the left side we're left with R divided by 5 so let's get rid of the 5 from the left side what's the opposite of divided by 5 dividing by 5 well multiplying by 5 so let's multiply both sides by 5 by 5 by 5 and we get R equals well 3 times 5 is 15 we isolated the variable and it equals 15 so on the left hand side I just want to mention we had R divided by 5 that last step and we times by 5 which would technically give us R over 1 or are divided by one which is just our this is isolating the variable right here if you get to multiplying that variable by one or dividing that variable by one so let's plug in that 15 and see if we get the correct answer here so I'm running out of room a little bit I'll fit it in here so 15 divided by 5 is 3 bring down an hour 8 and we end up with 3 plus 8 which gives us the 11 we want it so let's go over to number 3 here where we have 7 equals 16 minus 3e so the equation looks a little different than numbers 1 & 2 we have the variable on the right-hand side but it's the same exact thing that we did for numbers 1 & 2 so we need to isolate that e so undo that right side of the problem so let's get rid of the 16 first so we have a positive 16 on the right hand side so the opposite would be subtracting 16 in order to get rid of it let's do minus 16 on the left hand side as well so 16 minus 16 gives us at 0 7 minus 16 gives us a negative 9 we're left with negative 3 e on the right side so that's multiplication so we need to do the opposite of multiplication in order to get the e by itself so let's divide both sides by negative 3 negative 9 divided by negative 3 gives us a positive 3 and we're left with E over 1 which is the same thing as just E we isolated the variable so e equals 3 let's plug it back in and see if that works three times three is nine bring down our 16 16 minus nine does give us that seven that we are looking for on the left-hand side of that equation so we were correct e equals three and lastly number four so we have some parentheses in this one and we need to get Y by itself or isolate the variable Y so we have two times parenthesis Y minus eight and parenthesis equals 24 so we need to do the opposite remember we need to undo that side the left-hand side of the equation and we're going to actually divide both sides by two to undo that two that is outside of the parenthesis so two divided by two is one that gives us one outside of the parenthesis there which is just going to leave us with y minus eight because anything times one is just that number or expression itself so we just have Y minus eight and then 24 divided by two is 12 so now we have Y minus 8 equals 12 so we need to get rid of that minus eight undo that part of the left hand side of the equation in order to isolate the Y so we need to add 8 to both sides in order to isolate the Y so a minus 8 and a plus 8 gives us a 0 those cancel out so we're left with Y and 12 plus 8 gives us 20 so y equals 20 let's plug it back into the equation to see if this gives us the answer 24 that we're looking for 20 minus 8 is 12 bring down the 2 outside of the parentheses which means multiplication and 2 times 12 does give us that 24 that we wanted so there you have it there's how you solve two-step equations hopefully that helped thanks so much for watching until next time peace