Understand the basics to solve solve for a

all right so for a problem like this if you can understand an equation that looks something like this then you can go ahead and solve a problem that looks like that so let's go and focus on this one first let me show you how to approach a problem like this and therefore we'll use that understanding to apply it to something like this though it's way more confusing even though you know how to do this or at least we're going to make sure you know how to do this so in this case we need to solve for x and what we need to do when we're sumfrex is identify what operations are being applied to our variable X so first of all we're being multiplied by a negative 2. and then here we're actually adding A3 now a lot of times students will be like why are you adding well that's a positive 3 right so you actually are adding it now if you don't like the way that's written you can go ahead and rearrange the equation to a negative 2x plus 3 right you're not going to write minus three that's a positive 3. so you're going to write plus three so hopefully now you can see oh yeah you are adding the 3 to the negative 2x so now we're just going to use our inverse operations right using the properties of equality to solve for x so we always want to undo addition and subtraction first and once we undo addition and subtraction first on the property um on both sides now we've got to look at undoing a multiplication and division you can see now my X is being multiplied by a negative 2. so the inverse operation of multiplication is going to be division therefore I have a negative 1 is equal to X and I can just flip around if I want to read it as x equals a negative 1. okay this whole process is exactly what we're going to do here so in this case we have an A now this a is wedged in between a one-half and a t squared but guess what guys that really doesn't matter right just like you have a three times two it's the same thing as a two times three so we can rearrange this problem any way that we want to all right because again we want to solve for the a so just like how we always like to write numbers in front of the X right whatever variable you're trying to solve for put that over at the end then the other thing is this is a positive VT right just like that's a positive 3. but a lot of times students don't like looking at it like a three they want to rewrite it this way so what I'm simply going to do is just rewrite this equation for my variable that I'm solving is not going to be nested in between two variables and I'm going to put it at the very end and then also I'm going to rewrite the VT as a positive or A Plus VT so okay so now again we still need to solve for a now a lot of times when I'm teaching literal equations I tell students like to put a box around your a or you can underline it there's a lot of different things we can do but again a lot of different things we can do to like identify what the variable we're trying to solve for because you can see here when you're dealing with the literal equation you have a lot of variables so sometimes it's helpful just to like put a square around it just to remind yourself like oh yeah I'm solving for a all right then we ask her a question what operations are being applied to our a well it's being multiplied by one half t squared and it's being added to by VT so just like we did over here we undo addition and subtraction first so therefore I'm going to subtract avt on both sides now over here I could do 5 minus three that gave me 2. we like that right give us a number and now you're like oh why don't we have all these variables and you know in math we can't do that we don't know the value of T we D we don't know the value of v and T so therefore I'm just going to be left with a D minus avt all right I'll put that nice little box there around there again and now we just need to say all right now what is being applied to my a well now we have our multiplication and again what do we do with our multiplication we use the name for separation we divide right so we're going to undo multiplication of one half and t squared by dividing by one half t squared foreign now one thing that's a little bit important if I want to simplify this if I took the number let's say 5 and divided it by one half I could actually rewrite that by multiplying by the reciprocal and that's going to equal as a 10. so dividing by one half is the same thing as multiplying by a 2. now these T's could divide out right but then you but you still have to make sure you divide this T into both of these terms so I would caution you against trying to like divide this out I would rather leave this as a rational expression but you can go ahead and simplify this now to rewrite this as a I read this as a 2 D minus v t all over a t squared is now going to equal to a and again there's many other ways you could simplify this you could divide the t squared into both those terms you could distribute the 2T if you want to it all depends on what your teacher asks for or how you're being too instructed but hopefully this video makes sense for you it gave you some value and if it did I know you're going to love the next video I have for you here