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earboth · #9 January 7th, 2009, 12:49 AM

Quote:

Originally Posted by jstark

Triangle TUV has sides TU, UV, and VT. TU=6x - 11, UV=3x - 1, and VT=2x + 3. Describe the possible values of x.

Any help is appreciated. I've been trying to figure this one out for a while.

If and only if the given terms refer to lengths of the triangles sides you have to use the triangle inequality:

The triangle ABC has the sides a, b, c. Then

$a+b>c\ \wedge\ a+c>b\ \wedge\ b+c>a$

So you get:

$6x-11+3x-1>2x+3\ \wedge\ 6x-11+2x+3>3x-1\ \wedge\ 3x-1+2x+3>6x-11$

$x>\dfrac{15}7\ \wedge\ x>\dfrac95\ \wedge\ 13>x$

Therefore you know:

$\boxed{\dfrac{15}7 < x< 13}$