Question 949734

The following triangle RST has sides of length {{{x}}}, {{{2x}}}, {{{10 }}}as shown.
A) Find the three inequalities, which must be true based on the sides of the triangle.
1. {{{x<2x+10}}} 
2. {{{2x<x+10}}}
3. {{{10<2x+x}}}
B) Write a compound inequality on your results above.

Remember that side lengths also need to be positive. Thus, each side must
be greater than zero. Take the smallest side length to ensure this.

{{{2x < x+10}}}=> {{{2x-x < 10}}}=>{{{x < 10}}}
{{{10 < 2x+x}}}=>{{{10 < 3x}}}=>{{{10/3< x}}}

{{{10/3 < x <10}}}