WEBVTT
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Hi and welcome.
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My name is Anthony
Varela, and today we're
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going to talk about
equivalent equations.
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So we're going to
talk about what
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are equivalent equations, what
does it mean for two equations
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to be equivalent, and then, how
can I tell if two equations are
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equivalent?
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So when talking about
equivalent equations,
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two equations are equivalent if
they have the same solution set
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in each equation.
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So here's an example of two
equations that are equivalent.
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And I've written
down their solutions.
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In both cases, x equals 2.
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So let's go ahead
and show, then,
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that these have the
same solution set.
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So working with the
equation that we
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see on the left side of the
screen, 8 equals 3x plus 2,
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I'm going to plug in 2 for x.
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And now I have 8
equals 6 plus 2.
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8 equals 8.
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That's a true statement.
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So x equals 2 is a
solution for that equation.
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Let's go ahead and work
on our other equation,
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16 equals 6x plus
4 when x equals 2.
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This gives me 16 equals 6 times
2 plus 4, 16 equals 12 plus 4,
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and 16 equals 16 is
a true statement.
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So x equals 2 is a solution
for the equation on the right.
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So now you can see that
these two equations here
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can be considered
equivalent equations,
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because their solution
sets are the same.
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So how can we determine, then,
if equations are equivalent?
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Well, what we'll do, then, is
we'll solve for each equation
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and see if their solution
sets are the same.
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So here, I have two equations,
6x minus 2 equals 7,
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and 9x minus 4 equals 14.
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I want to know if these two
equations are equivalent.
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So let's go through the process
of solving each equation
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and then we'll compare
their solution sets.
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So in the first equation,
the one on the left,
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I'm going to add 2 to both
sides of the equation.
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So I have 6x equals 9.
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Well, now I need to divide
both sides of my equation by 6,
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and this will give
me x equals 1.5.
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So that's the solution to
the equation on the left.
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We need to solve the
equation on the right
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and see if we get x equals 1.5.
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So to solve first,
we need to add 4
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to both sides of the equation.
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So this gives me 9x equals 18.
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And then when you divide both
sides by 9, we get x equals 2.
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So now, comparing our
two solution sets,
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because 1.5 does not equal
2, these two equations
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are not equivalent.
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They have different
solution sets.
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So let's take a look
at another example.
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Our equation on the left
is 2/3x plus 7 equals 19.
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The equation on the right
is 1.5x minus 15 equals 12.
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Let's solve both
of these equations,
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and then we'll compare
their solution sets.
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So solving for the
equation on the left first,
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we subtract 7 from both
sides of the equation.
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So we have 2/3x equals 12.
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And now we need to
divide both sides by 2/3.
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And dividing by a
fraction, I find it easier
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to multiply by that
fraction's reciprocal.
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So I'm going to multiply by 3/2.
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That's the same as
dividing by 2/3.
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So that gets x on one
side of the equation.
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And then 12 multiplied
by 3/2 equals 18.
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So I've solved my
first equation.
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X equals 18.
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Let's see if x equals
18 as a solution
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to our second equation.
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So the first thing I
need to do is add 15
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to both sides of this equation.
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So 1.5x equals 27.
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And now I need to divide
both sides by 1.5.
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And I get x equals 18.
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So here, these two
equations are equivalent,
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because they have the
same solution set.
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And that's really
it for this tutorial
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on equivalent equations.
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Remember that equivalent
equations are equations
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that have the same
solution sets,
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so solve for each equation
and compare their solutions.
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If they have the same solutions,
they're equivalent equations.
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If they have different
solution sets,
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they are not
equivalent equations.
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Well, thanks for watching
this tutorial on equivalent
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equations.
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Hope to see you next time.