# TSI Math: Finding a Range of Solutions for a Variable in a Triangle's Equation

What is the range of all possible values of x for ∆DEF, if DE = 2x – 7, EF = 3x + 9, and DF = 2x + 5?

Geometry and Measurement | Plane Geometry |

Mathematics and Statistics Assessment | Plane Geometry |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Geometry and Measurement |

TSI Mathematics | Geometry and Measurement |

Test Prep | TSI |

### Transcript

and psych test takers everywhere are scrambling to determine a

little fact about this unholy union Like all heroes intent

on saving the universe from evil we need a strategy

Our strategy relies on the triangle inequality serum It says

that some of the lengths of any two sides of

a triangle must be greater than the length of the

third side Right Otherwise the triangle wouldn't touch so with

angle df we know that d plus e s greater

than d f e f plus d f is greater

than d e n d f plus d e is

greater than e f right So all the little side

thing he's touch will use this knowledge along with the

more algebraic definitions of the seides find all the possible

ranges of x let's start with d plus c f

his great of ndf and we'll get to x minus

seven plus three X plus nine is greater than two

x plus five But when we solve this inequality we

end up with yes x is greater than one right

Actually did all the math get point that x is

greater Next we have df plus cf scarier than d

e that gives us two x plus five plus two

extra stein's greater than to explain it's Seven solve it

and we get axes while greater than what is that

negative seven Yeah well this is obvious because we already

know that x is greater than once Of course it

has to be great the negative seven as well We

can't have a triangle with negative sides at least not

in this reality So lastly let's solve df plus de

is greater than e f and we get two x

plus five plus two extra money Seven is greater than

three x plus nine This will give us access great

event while eleven This inequality trumps the other two and

is the only one that matters and the value of

x can be anything It wants to be as long

as it's larger than eleven So the answer is d 00:01:57.456 --> [endTime] and yes we are shmoop oh snap