okay let's take a look at these four equations of course i have t plus two is equal to seven x minus five is equal to negative ten four y is equal to twelve and negative two thirds h is equal to six so when do you uh start learning how to solve equations like this well for most people it's going to be in a pre-algebra course uh of course you're going to see this again in algebra 1 and other type of algebra courses but you're certainly going to be kind of really introduced to solving algebraic equations in pre-algebra now a funny thing about this uh word pre-algebra it kind of implies that you're doing something other than algebra you're like doing the math before algebra but just to be clear when you're in a pre-algebra course you're in fact learning algebra okay so you're just not learning it at a complete full level uh like an algebra one course so you're just kind of taking a lighter version of an algebra class but indeed you are learning algebra so if you think you know how to solve these four equations go ahead and pause the video and put your answers into the comment section of course i'm going to solve these here in just one second but first let me quickly introduce myself my name is john i'm the founder of tablet class math i'm also a middle and high school math teacher i'm going to leave a link to my math health program in the description of this video but if you think you are a bad math student maybe you think you're not good at math maybe you don't feel like you're getting enough math instruction or you're not connecting to your teacher's teaching style whatever the case is whatever difficulty you're having in mathematics i'm telling you right now there is a solution okay i have yet met a bad math student and i've been teaching math for decades if you're struggling in math there's a reason behind there okay and whatever the reason is it can be solved but the most important thing you need is two things one you need the desire to learn you got to be willing to work hard and two you need the right instruction and i like to believe i have that right style of instruction because i like to really explain things in super easy understandable bite-sized pieces so anyone and everyone can learn math so if you're at the middle school high school or college level definitely check out my math health program if you're having a tough time in mathematics now if you're preparing for any kind of test that has a math section on it i'm talking about things like the ged s-a-t-a-c-t gre gmat asvab accuplacer clip exam maybe a teacher certification exam i can help you prepare and pass those exams if you home you definitely got to check out my homeschool math courses we were just voted number one from a major national publication in homeschooling for middle and high school math very proud of that achievement and if you don't have any math notes i'm going to leave links to my math notes in the description of this video as well but uh i got to tell you right now if you want excellent grades in mathematics you need to learn how to take excellent math notes so start improving your notes and everything will start getting better for you all right so let's get into these problems we have four basic equations and um each one of these equations to solve or to get the solution to these equations is going to require one step okay so there's one step now the step that we're going to be doing is going to be different for each of these equations but it's just going to be one step to get the solution so let's uh go down here real quick and talk about what you're going to be learning in pre-algebra and algebra 1 and beyond in terms of solving equations so think of it kind of as like steps like you're going to be climbing some steps and let me just kind of do it like this so the first type of equation you're going to be solving okay right here is called a one-step equation something like this 2x is equal to 8. we literally just have to take one step to get the answer so when you're studying like uh equations in pre-algebra and you can actually do a little bit of this even in more like middle school math uh in fact you were doing some of this stuff in elementary school you just didn't realize it but to get the solution to this equation it requires literally one step and that's what we're going to be practicing in this video now once you get these equations down you move on to what type of equations do you think we're going to be doing next if you said two steps well i tell you you that is very impressive it shows me that you're paying attention to the video so that's excellent so that would be an example of like say three y minus one is equal to eight okay so to uh solve this particular equation you need to take two distinct exact steps okay take well one step and then you take another step and you solve these type of equations so what do you think comes after two-step equations now if you said three-step equations that's a pretty good answer but in fact it's not the way we describe it okay i'm going to go ahead and erase my little stairs here what you really have is uh something called multi-step okay multi-step equations and that could be something like this let's say uh 2h minus 1 is equal to 7 h plus 2 times 2h plus 9. okay so i just wrote up just made something up but in order to solve this particular equation you're going to have to take multiple steps but if but the steps you're going to be taking are nothing more than a bunch of one-step type of uh procedures okay so whatever steps we learn here we're just kind of just doing two of them in this problem and then we're just doing a bunch of these same kind of steps in this particular problem so there is a couple of few other details but in general when you're learning how to solve equations this is kind of the path you're going to be taking so the type of equations you're going to be focusing on in this particular video are one step equations of course this is stuff that you really need to master at the pre-algebra level and then all of this is you know you get into like algebra 1 and of course algebra 2. okay so hopefully that kind of gives a little bit of the context of what what we're going to be doing here and we're going to start off with our first equation right here okay so again um we're talking about one step and what is this one step well here i could just show you this step but i really want to explain this to you okay well one thing you need to know is that an equation is like a balance scale okay it's like this there's a little fulcrum there or teeter-totter or see-saw whatever you want to say uh think of this thing always has to stay in balance so whatever you do to one side of the equation okay whatever step you take you have to take the exact same step on the other side of the equation you can take whatever step you want to do you can add subtract multiply divide as long as you do it equally to both sides you can never disrupt the balance of the equation okay so that's number one number two what is the goal of this equation or any equation well it's to figure out what the variable is equal to so here we have the variable t we want to figure out what t is equal to what number is t equal to and that particular number if we plug it into the equation this is a solution if in fact it balances this thing out okay so these are just big picture concepts that you need to know and keep in mind when you're solving any equation all right now as we get going here i'm going to show you how to do this in a second i want to really uh encourage you to follow my format to solve these equations it's probably the most typical uh format but there are a couple uh well there's like another way of writing showing your work don't do it this other way okay in this other way i'm not even going to mention it just do it my way it's probably the most common way anyways in terms of how you write this stuff out okay so let's get going here so we have t plus 2 is equal to 7. so i want t by itself remember t by itself that's the solution that's the goal so how can i get i have t plus 2. i got this plus 2 over here i'm like you know i don't want this thing next to the t i just want t by itself so how about we just subtract 2 from this 2. okay so if i have a positive 2 and i subtract the 2 from it that's zero it basically makes that go away but remember the rule in algebra whatever you do to one side of an equation you have to do the exact same thing to the other side so in this case we're going to subtract 2 from both sides of the equation okay and then what you're going to do is kind of add down in the column manner so t plus nothing is t okay by itself and then positive two minus two is zero so all we have over here is t okay t plus nothing is just t this goes away we don't need to write that zero and then 7 minus 2 is of course 5. now most of you probably saw that 5 was the solution here but what we're really practicing here is stressing the principles the mechanics the big concepts that you need to under truly really understand to solve any equation then we're starting off with these basic equations but again i want to emphasize you know hey whatever you do to one side you got to do to the other side and then this value right here is the solution if in fact if i plug it back into this uh if i replace a 5 with this t right there let's go and check the solution to make sure it's accurate so if i have t plus two is equal to seven i'm gonna replace this t with this five okay so let's do that now and then i'm gonna check my work all right so five plus two is 7 and 7 is equal to 7 that's a true statement so because when i replace this 5 okay with the t and i got the left hand side equal to the right hand side which of course is true that is in fact a valid solution to that equation okay so remember you know the mechanics is easy you could say oh plus 2 just subtract 2 from both sides get the answer yes you know i think um obviously i can make this like a one minute long video i could just do this these problems real quick but i'm really trying to stress here is for those who are studying basic equations is to really kind of understand the basics the fundamentals okay all right let's move on now we'll pick up the pace just a bit and now if you think you could do this problem okay this is very similar to the previous problem it's going to require one step and what do you think that first step is going to be okay well if you said well we got x minus 5 we want x by itself how about we uh get rid of this negative 5 by adding a 5 over here okay let me write that a little bit better so negative 5 plus 5 is 0. that gets this x all by itself on the left hand side so i can add a 5 over here okay remember i want to keep this format then you're going to be adding down in a column manner so x plus nothing is x or write that right there negative 5 plus 5 is 0. we don't need to write that zero just kind of vanishes and now i have negative 10 plus five is negative five that is the solution now you can see here that you need to understand positive and negative uh number rules so this is definitely a big deal at the pre-algebra level in like at the eighth grade math level make sure you understand how to add subtract multiply and divide uh positive and negative numbers okay so hopefully this didn't trip you up but if you were kind of confused about this well then make a mental note and go back and reviews let me give you a couple suggestions one i have tons of videos on my youtube channel my pre-algebra playlist on this more basic level of algebra and positive negative numbers etc or i teach this super thoroughly in my pre-algebra course as well okay so let's move on to our next problem all right again uh you could just see here all we're doing is taking one step the first the one step is just adding five to both sides we got the uh solution here we're subtracting both sides we got the solution so let's move on down here and continue on with these one steps so what is this equation well it's 4y is equal to 12 but what does this mean in algebra this 4 in front of the y means multiplication now let me go back over here i've kind of uh missed a point and i want to kind of bring this in now notice in our equation right here when we have t plus 2 okay t plus 2 is equal to 7 we ended up the step that we took involves subtraction okay so when we saw an addition we ended up using subtraction to get to that solution okay so that's what we call it inverse operation now notice over here when we had subtraction x minus 5 we ended up using addition to get to the solution all right so keep that in mind because this is very very important and over here we have um 4 times y this means uh when you have a four or a number in front of a variable this means multiplication okay so what is going to be the inverse of multiplication what do you think the inverse uh what's the opposite um operation mathematical operation that you would associate with multiplication well hopefully you said is it division you would be correct so just like addition it's inverse is subtraction with subtraction it's inverse is addition for multiplication its inverse is division and with division its inverse is multiplication okay so this is another thing that you want to kind of remember when you're solving these basic equations so we're dealing with the multiplication here we want to undo this and just get y by itself so i know now that you know that this is multiplication you're thinking division all right like okay what's the one step we can do here hopefully he said oh i could just divide this side of this equation by 4 because 4 divided by 4 is 1 okay 1 y that's what i want now we don't write variables like 1y like this we just write it like this y this means 1y so i got to this y by dividing whatever this number is i just divide it by itself on this side of the equation i get 1y or y and that's exactly what i want so let me go ahead and uh put that here but again let's remember the rule okay whatever you do to one side of the equation you got to do the exact same thing to the other side so we have 12 divided by four which of course is three there's our one step and there is our solution okay so hopefully you're getting pretty comfortable with this and i i saved the uh the most challenging one or the one x that tends to confuse students the most so let's take a look at this problem so what does this mean well i have negative two-thirds times h now i'm going to write this a little bit differently here negative two over 3 times h uh it's really i'm just writing this this way it's just to make this a little bit easier for you to see the the way you're writing these fractions right here this way with a little slash or with a little uh uh kind of complete horizontal bar doesn't make a difference both are perfectly fine but let's take a look at this okay so we have negative two thirds times h so you might be thinking to yourself well this is multiplication because this is this number times this so maybe we need to divide both sides of the equation by this number okay whatever that number in front of that of that variable so maybe we need to do this negative uh divide both sides equation by negative two thirds and if you uh we're thinking in these terms to solve this equation you would be correct okay so that's good that's very good a matter of fact this will get you the right answer but i want you to uh kind of uh key in on something else here let's go back to this previous problem and remember this problem here involved multiplication so we say okay multiplication is division now in this next problem we're going to be doing really what we've got is a division problem so we can use multiplication to do this so let me show you how we want to kind of think about this and let me use this version of the problem okay so we have negative uh 2 divided by 3 okay so what's the goal to solve this well we want to get h by itself so this right here is division okay there is multiplication going on but i want you to kind of think of it as division problems so we want to use multiplication to get to the solution it's the easiest way to remember how to do this so let's take a look at what's going on here so we have this fraction negative 2 divided by 3 or negative 2 thirds if i multiply this side over here what i'm going to do is i'm going to flip this fraction so that's going to be 3 over 2 and i'm also going to keep the sign negative 3 over 2 and i'm going to multiply by this negative 2 thirds okay any time you multiply a fraction by it's what we call it's reciprocal if you flip it upside down you're always going to get 1. a negative times negative is a positive and then 3 times 2 is 6 over 2 times 3 is 6 so 6 over 6 is 1 we're gonna get one h and that's what i want i want an h all by itself so uh over here the easiest way to handle problems when you have a fraction coefficient in other words a fraction in front of a variable it's just to flip that fraction upside down and multiply both sides of the equation by that reciprocal i.e that fraction that we flipped upside down and you need to keep that sign as well so if it's negative keep uh the negative in that reciprocal in other words if this is negative you have to multiply both sides equation by that negative fraction if it's positive you're going to multiply by the positive version of that all right so let's go ahead and do this math so 6 times negative 3 over 2 so that's 6 over 1 right so 6 times negative 3 over 1 times 2 which of course is 2. 6 times negative 3 is negative 18 negative 18 divided by 2 is negative 9 okay so this is negative 9. again you need to know your positive negative numbers and how to work with fractions to do these basic one-step equations and i'm actually going to be posting a video very very shortly about the math you need to know uh to be successful in pre-algebra okay so again we're taking pre-algebra we're looking at pre-algebra type of equations which you need to know for algebra one but to be successful in pre-algebra you need to know all that stuff in middle school math which would include the basics of positive negative numbers fractions and some additional things as well so whatever basic skill you know you are not quite understanding just make a mental note of it and go back and review but if you understood all of this okay right now and you're like yeah i just wanted to check myself and see if i got this not only got the answers right but really truly understood uh the steps you need to take and the concepts behind it then i must go ahead and give you a good old 1984 mohawk i got to throw some colors in because you know these mohawks were pretty impressive back in the day i didn't wear one okay but i did have a lot of friends who uh wore one and we always thought that was pretty cool but let me go ahead and throw in an a-plus nice job okay so remember uh when you're learning how to solve equations you got to master these basic ones first okay these one-step equations and if you have any weak areas that come out i.e your little rusty on positive negative numbers fractions whatever the case might be make a mental note and go back and bolster those skills because that's you know if you don't get this down all these misunderstandings are going to start compounding and you're really going to have a very difficult time in the more advanced equations uh two-step and multi-step equations but uh hopefully this little video was a nice little review for you and if that is the case go ahead and review how to smash that like button okay that definitely would help me out and if you're new to my youtube channel hopefully you'll consider subscribing i've been on youtube for 10 plus years i have over a thousand plus math videos basic math to advanced math like calculus and everything in between so if you like my teaching style please take advantage of all my content but my best math help will always be within my math help program okay so with that being said i definitely wish you all the best in your mathematics adventures thank you for your time and have a great day