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TSI Math: Finding a Range of Solutions for a Variable in a Triangle's Equation 45 Views
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Description:
What is the range of all possible values of x for ∆DEF, if DE = 2x – 7, EF = 3x + 9, and DF = 2x + 5?
Transcript
- 00:02
Okay next time for shoppers What is the range of
- 00:05
all possible values of x for angle df if d
- 00:10
is to explain a seven e f is three x
- 00:13
plus nine and gf is two x plus five Okay
- 00:20
interesting problem here Three lines have met forming a triangle
Full Transcript
- 00:24
and psych test takers everywhere are scrambling to determine a
- 00:27
little fact about this unholy union Like all heroes intent
- 00:31
on saving the universe from evil we need a strategy
- 00:33
Our strategy relies on the triangle inequality serum It says
- 00:37
that some of the lengths of any two sides of
- 00:39
a triangle must be greater than the length of the
- 00:42
third side Right Otherwise the triangle wouldn't touch so with
- 00:45
angle df we know that d plus e s greater
- 00:48
than d f e f plus d f is greater
- 00:50
than d e n d f plus d e is
- 00:52
greater than e f right So all the little side
- 00:55
thing he's touch will use this knowledge along with the
- 00:57
more algebraic definitions of the seides find all the possible
- 01:00
ranges of x let's start with d plus c f
- 01:03
his great of ndf and we'll get to x minus
- 01:05
seven plus three X plus nine is greater than two
- 01:08
x plus five But when we solve this inequality we
- 01:11
end up with yes x is greater than one right
- 01:14
Actually did all the math get point that x is
- 01:16
greater Next we have df plus cf scarier than d
- 01:19
e that gives us two x plus five plus two
- 01:21
extra stein's greater than to explain it's Seven solve it
- 01:24
and we get axes while greater than what is that
- 01:26
negative seven Yeah well this is obvious because we already
- 01:29
know that x is greater than once Of course it
- 01:31
has to be great the negative seven as well We
- 01:33
can't have a triangle with negative sides at least not
- 01:36
in this reality So lastly let's solve df plus de
- 01:39
is greater than e f and we get two x
- 01:41
plus five plus two extra money Seven is greater than
- 01:44
three x plus nine This will give us access great
- 01:46
event while eleven This inequality trumps the other two and
- 01:50
is the only one that matters and the value of
- 01:52
x can be anything It wants to be as long
- 01:55
as it's larger than eleven So the answer is d 00:01:57.456 --> [endTime] and yes we are shmoop oh snap
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