Atriangle has sides measuring 5 inches and 8 inches. if x represents the length in inches of the third side, which inequality gives the range of possible values for x? .

Hey! So, in doing this, we need to follow the rule for the 3rd angle of a triangle that x has to be greater than 0. So, to solve this you need to do the equation x = perimeter-side-side. We only know the 2 sides, so plugging in the numbers, you get x = perimeter - 5 - 8. Doing this, if we set the perimeter to  anything below 17, then x will be lower than 0. So, by setting the perimeter to 17, we get that x can equal 4. Now, if we set the perimeter to the highest it can be for x > 0 to be true, we get 12. So, putting that into an expression, we get  x  > or = to  4 and x  < or = to 12. Thanks!

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