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8/8/2019 3-3 Literal Equations
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Good grief.Good grief.MoreMore
equations?equations?
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Isolating the Variable inIsolating the Variable in
Literal EquationsLiteral EquationsNotes for October 26 th
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Literal EquationsLiteral Equations Just a whole bunch of letters!
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Literal EquationsLiteral Equations An equation comprised only of variables!
That means it is all letters!!!
Only variables?!Only variables?!
What does thatWhat does that
mean?mean?
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Literal EquationsLiteral Equations Literal equations is the fancy word for
formula
A formula is an algebraic expression relatingtwo or more quantities
For example:
The f ormula f or area o f a rectangle is A = bh
The f ormula f or the volume o f a prism is V = Bh
The f ormula f or distance is d = rt
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The Goal of Literal EquationsThe Goal of Literal Equations Isolate (solve for) a particular variable
This means that you must get the variable
you¶re solving f or all by itself on one side o f
the equal sign
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K ey Point:K ey Point: By definition, variables represent numbers.
Therefore (and this is K EY), variables have
the same properties as numbers «
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Variables can move too?! SoVariables can move too?! So
they have to cancel each otherthey have to cancel each otherout. I think that is calledout. I think that is called
inverse operations, right? Caninverse operations, right? Can
we review those?we review those?
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To make a variable go boomb «To make a variable go boomb « You must do the inverse (opposite) operation
v
v
z
z
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So here we go «So here we go «
You guys are practicing? Huh,You guys are practicing? Huh,
interesting. Perhaps I should tryinteresting. Perhaps I should try
that. Then maybe I won¶t throw sothat. Then maybe I won¶t throw somany interceptions against themany interceptions against the
Browns.Browns.
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Solve forSolve for x x
53 ! x3533 ! x
2! x
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Now we will do the exact same thing «Now we will do the exact same thing «
But with letters!But with letters!
Solve for a
cba!
bcbba !
bca !
Get rid of theGet rid of the
constantconstant
(subtract)(subtract)
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Now let¶s discussNow let¶s discuss How were these two problems similar?
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Solve forSolve for x x
64!
x
46)4
(4 v! x
24! x
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Now we will do the exact same thing «Now we will do the exact same thing «
But with letters!But with letters!
Solve for a
cb
a!
bcb
ab !)(
bca !
Get rid of theGet rid of the
coefficientcoefficient
(multiply)(multiply)
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Now let¶s discussNow let¶s discuss How were these two problems similar?
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Solve forSolve for x x 305 ! x
5
30
5
5! x
6! x
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Now we will do the exact same thing «Now we will do the exact same thing «
But with letters!But with letters!
Solve for b cab !
a
c
a
ab!
a
cb !
Get rid of theGet rid of the
coefficientcoefficient
(divide)(divide)
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Now let¶s discussNow let¶s discuss How were these two problems similar?
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Solve forSolve for x x 273 ! x72773 ! x
93 ! x
3
9
3
3
!
x
3! x
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Now we will do the exact same thing «Now we will do the exact same thing «
But with letters!But with letters!
Solve for b d cab !
cd ccab !
cd ab !
a
cd
a
ab ! a
cd b
!
Start byStart by
cancelling thecancelling theconstantconstant
Now get rid of Now get rid of
the coefficientthe coefficient
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Now let¶s discussNow let¶s discuss How were these two problems similar?
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Final ExampleFinal Example Solve for c bca 5!
b
bc
b
a
5
5
5!
b
a
c5
!
R emember, the coefficient isR emember, the coefficient is
every term that is not theevery term that is not the
variable you are isolating!variable you are isolating!
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Now go practice, because this isNow go practice, because this is
probably the hardest thing that youprobably the hardest thing that youhave ever done. K ind of like tryinghave ever done. K ind of like trying
to get my Saints back to a winningto get my Saints back to a winning
streak streak ± ± one of the hardest thingsone of the hardest things
I¶ve ever done.I¶ve ever done.
