WEBVTT
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Today we're going to talk
about literal equations.
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So we'll start by talking about
what a literal equation is,
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and then we'll do some examples.
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So let's start by reviewing
the idea of an equation.
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An equation is just
a statement that
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says that two
quantities are equal.
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So for example, the
equation 12y minus 8
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equals 40 says that the
expression on the left, 12y
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minus 8, has the same
value as the expression
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on the right side
of the equals, 40.
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We have another
example of an equation
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9a squared minus b
squared equals 15.
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And this type of equation
is called a literal equation
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because it has more
than one variable.
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However, even in a
literal equation,
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the expression on the left side
of the equals has to equal,
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or has the same value,
as the expression
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on the right side
of the equal sign.
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And we use literal equations
all the time in math.
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For example, the
equation y is equal to mx
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plus b is another example
of a literal equation.
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A common type of literal
equation is a formula.
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So for example we
have the formula
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for the area of a rectangle.
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A is equal to l times w, where
A is the area of the rectangle,
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l is the length of the
rectangle, and w is the width.
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And depending on what
information you're given,
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you might want to rewrite a
formula in a different way.
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So for example, if I
wanted to use the formula
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to solve for the width, I want
an equation that starts with w
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equals, or has w isolated
on one side of the equation.
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So I could rewrite this
by dividing both sides
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by l, which would give me that
w is equal to the area divided
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by the length of the rectangle.
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We could do the
same thing to find
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in the equation for the
length of the rectangle.
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We would do that by
dividing both sides by w
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to isolate the l variable.
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So we see that the
length of a rectangle
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is equal to the
area over the width.
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Let's look at another example of
a formula, a literal equation.
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I have the formula for
the area of a circle,
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a is equal to pi r squared.
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So I can rearrange this formula
to have an equation that
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has r isolated by itself.
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So we're solving in terms of r.
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So with my equation, to
isolate the r variable,
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I'm going to start by
dividing both sides by pi.
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So then I have A over pi
is equal to r squared.
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And then to cancel
out the 2 exponent,
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I'll take the square
root of both sides.
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And I found that my radius
is equal to the square root
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of the area of the
circle divided by pi.
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Let's look at the literal
equation, the formula,
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relating the variables
distance, rate, and time.
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So we can say that distance
is equal to the rate
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times the time, but we can
also rewrite this equation
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in terms of the
rate and the time.
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So to find an equation
in terms of the rate,
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I'm going to isolate
the r variable
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by dividing by t on both sides.
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So I found that the rate is
equal to the distance traveled
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over the time.
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I can do the same thing to
solve for the time variable, t.
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So to do that I'll
divide both sides by r,
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and I found that time is
equal to the distance traveled
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divided by the rate, or the
speed that you're traveling.
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So finally let's look at the
Pythagorean theorem, which
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says that a squared plus b
squared equals c squared,
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where a and b are the
legs of a right triangle,
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and c is the hypotenuse
of a right triangle.
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So we can write this
formula, or this equation,
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in terms of each side
length, a, b, and c.
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So first, if I want to
write this in terms of a,
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I'm going to start
by subtracting
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b squared from both sides.
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So this will give
me a squared is
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equal to c squared
minus b squared.
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And then to cancel
out the two exponents,
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I'll take the square
root of both sides.
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So I'm left with a is equal to
the square root of c squared
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minus b squared.
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Let's do the same
thing and solve
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for-- write an equation in
terms of the side lengths of b.
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So to isolate the
b variable, I'm
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going to subtract a
squared from both sides.
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This will give me b
squared is equal to c
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squared minus a squared.
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And then I'll take
the square root again
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to cancel out the 2 exponents.
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So I find that b is equal to
c squared minus a squared.
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So we can guess that c then
will be equal to something
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with a squared and b squared.
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But it's going to
look a little bit
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different than these
equations because we already
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have c squared
isolated by itself.
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So then to just get
c by itself, we only
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need to take the square root.
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So we found that c is equal
to a squared plus b squared.
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So let's go over our
key points from today.
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Literal equations
are equations that
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have more than one variable.
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Formulas are literal
equations and are used often
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in mathematics.
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Depending on what kind of
information you are given,
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you may wish to express
literal equations or formulas
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in different ways.
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So I hope that these
key points and examples
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helps you understand
a little bit more
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about literal equations.
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Keep using your notes
and keep on practicing,
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and soon you'll be a pro.
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Thanks for watching.
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