Please help :(
The lengths of two of the sides of a certain triangle are (x - 3) and (x+3) where x 3. Which of the following ranges represent all of the possible values of the third side, s?

Question

Please help :(
The lengths of two of the sides of a certain triangle are (x - 3) and (x+3) where x > 3. Which of the following ranges represent all of the possible values of the third side, s?

paxpolaris · Answer

The sum of any two side of a triangle have to be greater than the third side.

paxpolaris · Answer

So, $$\large(x-3)+(x+3) >s$$$$\large(x-3)+s >(x+3)$$$$\large\cancel{(x+3)+s >(x-3)}$$

use the  first two inequalities to find the limit for s

anonymous · Answer

why not the last one? does it cancel out or something?

paxpolaris · Answer

we already know that   $x+3>x−3$ .... so the last one happens to be true for all s ... it doesn't help

anonymous · Answer

ohh, okay. So would the answer be 6 < s < 2x ?

paxpolaris · Answer

yes $\Large\checkmark$

anonymous · Answer

Thank you so much :) I really didn't know what to do for it so you helped me SO much :)