Literal Equations
Summary
TLDRIn this Missmi Math Tutorials video, Miss Smith introduces literal equations, which involve solving for one variable amidst multiple variables in an equation. She emphasizes the importance of identifying the target variable and suggests treating extra variables as numbers to simplify the process. Through examples, she demonstrates how to isolate the desired variable by performing inverse operations and maintaining equation balance, resulting in a solution that may not be 'pretty' but is accurate. The video aims to demystify literal equations and equip viewers with the confidence to tackle them effectively.
Takeaways
- 📚 Literal equations involve solving for a specific variable amidst multiple variables in an equation.
- 🖍️ It's important to identify and highlight the variable you are solving for to keep your focus clear.
- 🔍 Pretend the variables are numbers to simplify the process of isolating the variable you're solving for.
- ⚖️ Balance the equation by performing inverse operations on both sides to cancel out terms.
- 🔄 When isolating the variable, move all other terms to the opposite side of the equation.
- 📉 Literal equations may not result in a 'pretty' answer, but the goal is to isolate the desired variable.
- 🔄 Division is used to eliminate coefficients in front of the variable you're solving for.
- 📝 Rewrite the equation in standard form to make it easier to identify and combine like terms.
- 📉 Constants and variables can be separated and simplified if possible.
- 📌 Treat special symbols like pi as a variable in the context of the equation.
- 🔗 Remember that what you do to one side of the equation must be done to the other to maintain equality.
Q & A
What is the main focus of the tutorial video by Miss Smith?
-The main focus of the tutorial video is to teach how to solve literal equations, which involve more than one variable and require isolating the variable specified in the problem.
Why is it important to identify the variable you are solving for in a literal equation?
-Identifying the variable you are solving for helps you focus on isolating that variable, making it easier to solve the equation by treating other variables as if they were numbers.
What strategy does Miss Smith suggest for dealing with multiple variables in a literal equation?
-Miss Smith suggests pretending the variables are numbers and focusing on isolating the variable you are solving for, regardless of the presence of other variables.
Why does Miss Smith recommend getting the variable you are solving for alone on one side of the equation?
-Getting the variable alone on one side simplifies the process of solving the equation, as it allows you to concentrate on the necessary operations to isolate that variable.
What does Miss Smith mean by treating variables as if they were numbers?
-Treating variables as if they were numbers means performing mathematical operations on them without getting confused by their presence, just as you would with numerical values.
How does Miss Smith approach moving variables from one side of the equation to the other?
-Miss Smith recommends performing the inverse operation on the variable to move it to the other side of the equation, ensuring that the operation is applied to both sides to maintain equality.
What is the significance of standard form in solving literal equations?
-Standard form, where variables are placed before constants, helps in organizing the equation and makes it easier to identify like terms and perform necessary operations for solving.
Why is it necessary to perform the same operation on both sides of an equation?
-Performing the same operation on both sides of an equation ensures that the equality is maintained, which is a fundamental principle in solving equations.
How does Miss Smith handle terms that cannot be combined in an equation?
-If terms cannot be combined because they are not like terms, Miss Smith suggests rewriting the equation and proceeding with the operations that can be performed to isolate the variable of interest.
What does Miss Smith advise when dealing with fractions in literal equations?
-Miss Smith advises multiplying both sides of the equation by the denominator to eliminate the fraction, which simplifies the process of isolating the variable.
How does the presence of the variable 'pi' affect the solving process in literal equations?
-In the context of the video, 'pi' is treated like any other variable, and the focus remains on isolating the specified variable, with 'pi' being part of the operations needed for solving.
Outlines
📚 Introduction to Literal Equations
In this segment, Miss Smith introduces the concept of literal equations, which involve solving for a specific variable amidst multiple variables within a mathematical problem. The emphasis is on understanding how to isolate the variable of interest, even when faced with a more complex equation. The tutorial suggests a strategy of treating variables as if they were numbers to simplify the process. The example given involves moving terms across the equation to isolate 'x', demonstrating the importance of performing inverse operations to cancel out terms and achieve the desired variable on its own.
🔍 Isolating Variables in Literal Equations
This paragraph delves deeper into the process of isolating variables in literal equations. It discusses the strategy of moving terms to one side of the equation to focus on the variable that needs to be solved for, in this case, 'y'. The video script explains the importance of performing inverse operations, such as subtraction and division, to cancel out terms and simplify the equation. It also highlights the concept of treating all terms as if they were numbers, even when they include variables like 'pi', which is treated similarly to a variable in this context. The summary includes an example where the equation is manipulated to isolate 'y', and the process of simplifying the equation is described in detail, including the handling of fractions and the use of standard form.
Mindmap
Keywords
💡Literal Equations
💡Variable
💡Isolate
💡Inverse Operation
💡Combining Like Terms
💡Divide
💡Standard Form
💡Pretend
💡Simplify
💡Pi (π)
💡Algebraic Manipulation
Highlights
Introduction to literal equations and their purpose in testing the understanding of solving for a particular variable.
The concept of literal equations involving more than one variable and the strategy to solve for the specified variable.
Highlighting the importance of identifying the variable to solve for and using visual aids like color to focus on it.
The strategy of treating variables as numbers to simplify the process of isolating the desired variable.
The preference for placing the variable to be solved on the left side in literal equations for ease of solving.
Demonstration of moving variables and constants across the equation to isolate the desired variable.
Explanation of the inverse operation to cancel out terms and isolate the variable.
The process of dividing by a coefficient to isolate the variable and the importance of maintaining the equation's balance.
The challenge of not being able to combine unlike terms and the approach to rewrite the equation accordingly.
The method of simplifying the equation to get the variable alone, even if the final answer isn't a 'pretty' one.
A step-by-step walkthrough of solving a literal equation for variable 'y', including moving terms across the equation.
The importance of writing in standard form when rewriting equations to maintain clarity.
The process of dividing each term by a coefficient to isolate 'y' and simplify the equation.
The handling of negative numbers and the conversion of the equation to a positive form for simplification.
An example of solving a literal equation involving the constant pi, treating it like a variable.
The technique of multiplying by the denominator to eliminate fractions in an equation.
The final steps of isolating the variable 's' in an equation involving pi and demonstrating the cancellation of terms.
The conclusion emphasizing the basic rules of solving equations and the importance of not being tricked by extra variables.
Transcripts
[Music]
welcome to missmi math tutorials I'm
Miss Smith in this video we're going to
be talking about literal equations it
tests you on how well you know you're
solving to get to a particular variable
that you're solving for so literal
equations changes it up where you've got
more than one variable within a problem
now it'll tell you what it wants to
solve for so in number one you'll it
wants you to solve for x but you've got
some other variables thrown in there so
you're not going to be able to get a
really nice pretty you know xal 3 you're
not going to get an answer like that
it's going to be a little Messier but
your goal is really just to isolate the
variable that they're asking for so for
number one you'll see that they're
asking for X so I think it's a good idea
to go ahead and just either highlight or
Circle or use a color pencil or
something and just know what it is
they're wanting you to solve for so you
can really look at it and think okay how
can I get that X alone and really the
best strategy is just to pretend these
are numbers pretend they're not
variables I know it looks scarier when
there are letters extra letters thrown
in there but just pretend they're
numbers Pretend This B is really a six I
want to get the X alone the easiest
first step is going to be to get my B
over to this side now I told you in some
of the last videos I always like to get
the variable we're solving for alone on
the left when you're talking about
literal
equations it's really just your
preference so when I'm doing literal
equations I'm going to go with whatever
is easiest but definitely when we're
solving regular equations or
inequalities get the variable to the
left literal equations just kind of go
with whatever's easiest I think it's
going to be easiest to just leave the X
where it is in this case and get
everything else over to the left so
let's start with a B this is a plus b so
we need to subtract B right I want to do
the inverse operation the opposite
operation so that these cancel to zero
but what I do to one side I have to do
to the
other now you might say oh I I can't
combine that 6 minus B those aren't like
terms and you're right we can't so
that's okay we just rewrite them I just
write 6 minus B
equals and I still have my MX and
remember X is what I'm trying to solve
for so this is really M * X I know that
because they're hugging each other up
close so I need to
divide to split them up and I want the m
to be the one that goes away right I
want that to reduce to one what I do to
this side I have to do to this
side so you'll notice now now my X is
alone I can't combine 6 and M I can't
combine negative B and M none of those
are like terms so I'm just going to
rewrite this as x = 6 -
B over
M so remember I said we're not going to
get a final pretty answer we're just
really moving things around to get the
variable we want alone that's all this
is and my second one it wants to solve
this equation for y so I'm going to just
highlight my y so remember that's what
I'm trying to get
alone so in this case it's going to be
easier I think to leave the variable on
the left side and get everything else on
the right I'm just going to go with
whatever is easiest so instead of trying
to separate this4 and Y first let's move
this 3x over let's just keep it simple
so this is a plus 3x so I want to do the
inverse I want to subtract 3x I want
that to cancel to zero what I do to this
side of the equation I have to do to
this
side so let me bring down what I have
left I've got -4
y equals now I can't combine 12us 3x
those are not like terms I'm just going
to rewrite it and I'm G to be careful to
rewrite it in standard form so I'm going
to put the -3x first then the positive
12 remember in one of my first videos we
talked about standard form and having
your variables first and your constant
second and so looking back at here I
should probably go ahead and switch that
so I could rewrite this as NE b + 6 over
M so coming back over here I subtracted
my 3 x i I rewrote it because I couldn't
actually combine these two
terms now I want to still get my y alone
now that's a -4 * y so I want to do the
inverse I want to divide by -4 because I
want those to cancel to one now what I
do to one side I have to do to the other
side now some teachers prefer to write
this whole thing over4 you can totally
do that personally I like to show that
each
term is being divided by -4 I think it's
just kind of easier to see when we can
combine things and maybe simplify or
reduce them and we definitely can here
so let's reduce what we can I've got my
y alone which is what I
want could I reduce -3 over -4 um in
terms of the numbers no 34s is as low as
it goes but but remember that a negative
/ a negative is a positive so I can go
ahead and make this a positive 34
x now this is pos2 / -4 so that's going
to be
A3 so I was able to get my y
alone in this last example hopefully
you'll recognize this sign this is pi um
it's 3.1 4 so on so forth um so we just
represent that with the symbol pi don't
let the pi scare you we treat it in this
case kind of like it's just another
variable we want to in this case it's
wanting us to solve for S so I'm going
to highlight what I'm solving
for the
S and I want to get the S alone and this
in this case I'm going to keep the S
over on the right side I'm going to try
to get all this other stuff over to the
left one step at a time remember I told
you guys in a recent video that we can
easily get rid of a fraction by
multiplying by the denominator so in
this case my denominator is
360 If I multiply this whole thing by
360 those
cancel but what I do to this side I have
to do to this side so that means I also
have to multiply that a by 360
so let me bring down what I have left
I've got
360a
equals pi r 2 s so notice all I did was
I knocked out that denominator to make
this a little better to look
at so now I'm solving for S so what this
means is pi * r s Time s so if I want to
isolate the S I just have to
divide by the pi and the r s the pies
will cancel the r squares will cancel
now I'm just left with s but what I do
to this side I have to do to this side
I'm going to say that probably 20
million more times in this unit and for
the whole rest of this class so just get
used to it so let me rewrite what I've
got here and I want to make sure I
simplify if I can but looking at this I
know I can't simplify any of that none
of it's like terms so I'm going to bring
down my S
equal 360 a 360 * a over p r
2 so there would be my final answer and
I didn't Square my final answer there
okay so that is literal equations again
you're just using your basic rules of
solving it's just thrown a couple extra
variables in there to try to trick you
but don't let it this has been M Miss
math tutorials
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