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Good day students welcome to mathgotserved.com in this clip were going to be going over how to solve multistep equations let's write down the quick the instructions for problems we are to solve each equation okay for problem number one we have the equation is the plus six X is equal to X minus seven minus eight now before ever so we can equation is beneficial to examining what type of equation you have secant know what you possible answer is are going to be now this is outbreak equation with variables on both sides Moammar you have an equation with variables of both sides you do not always have a solution okay if you have one unique solution you can have infinitely many solutions or you can have no solutions that all okay we need an example of how your answers will look like in the three cases the case of Y the have one solution your answer is going to look something like this you have X equals the number line X equals two you can also have infinitely many solutions so infinitely many solutions if you have infinitely many solutions your answer is going to look like this for equals for you end up with identity is true statement know variables of any sort in your final step and then lastly when solving equations with variables on both sides you can have no solutions know solutions an example of the situation we have the solutions is three equals five what you notice notice about this this is a all six the so when you so one of the equation in in the fall statements the know that there are no solutions okay so you have to keep this in mind anytime you solving algebraic equations with variables on both sides such as this okay go ahead and solve this equation and see if we will have one solution no solutions or infinitely many solutions now the first you want to do is you want to collect all the variables on one side and all the constants on the other side now a variable that is not have a coefficient within a given the default coefficient of one like in this case this variable doesn't have a coefficient so the one in front of the okay now let's collect all the X is to the left and have all the numbers to the right before we do that you noted that I can simplified is right side the low this first let's rewrite this fifteen plus six X equals one X minus seven minus eight decided is saying so we accurate the sign negative fifteen now let's collect all the X to the left and the constants on the right this is positive one so you going to subtract one X from both sides of the equation okay right subtracted one next this as up to zero now this is positive fifteen were going to do is going to add fifteen to both sides of my equation actual and going to subtract so subtract fifteen because this is positive fifteen so subtract fifteen from both sides of the equation now let's see what happens here the goal is the one variables on the left and constants on the right now you notice these two are opposites of the out of to zero positive six minus one X is five X positive five X on the right side these two are opposites the out of to zero now negative fifteen minus fifteen the sides of the same so we added keep the sign third now what you notice we have collected all the X is to one side combine them in the process you have all the numbers combine on the other side of the equation now to finish this off will simply divide both sides by five to isolate X and then we'll have X equals negative six okay so which of these types of solutions that this result six is this option one we have one unique solution now let's do a quick check just to make sure that our answer is in fact correct so is a check now how do we check our work will simply plug our results into the original equation and see if we end up with a true statement okay so you have fifteen plus six is that X up with my solution there equals X minus seven so is that X will with negative six minus seven minus eight now this is terms out to be true statement then our results is in fact correct okay so you have fifteen positive six times negative six is negative thirty-six equals now negative six we can combine negative seven minus eight which is negative fifteen fifteen minus thirty-six combine these two we will get negative twenty-one in any to combine these two have negative twenty-one so is negative twenty-one equals negative twenty-one answer is yes so the confidence that our answer is in fact correct okay right now let's box our final answer in one two question number two okay number two we have on mother multistep equation for times why plus seven plus four times why minus one equals eight why minus eight why okay what you notice about this equation it has variables on both sides so this is this equation has variables on both sides there can

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