SOLUTION: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18cm and a second side that is 3cm less than twice the

The three sides are:  

First side   = 18
Third side   = x
Second side  = 2x - 3

First side  + Second side > Third Side,   therefore   18 + (2x - 3) > x     
First side  + Third side  > Second Side,  therefore          18 + x > 2x - 3
Second side + Third side  > Second Side,  therefore    (2x - 3) + x > 18 

So we have:



Simplifying:


Simplifying further:


Simplifying further:


Simplifying further:


We can eliminate the first inequality, since the third one guarantees it
because if x is greater than 7 it is CERTAILY greater than =15.


Those two inequalities can be combined as



or if we prefer:

, which is the same thing.

So the third side, x, is greater than 7 but less than 21.

Since the Second side is 2x - 3, we must build 2x - 3
from the x which is in the middle of .

To make the x into a 2x, we multiply all three sides of

 by 2, getting

,

To make the 2x into a 2x - 3, we subtract 3 from all three sides of the above:



Simplifying



So   

So the Second side, 2x - 3, is greater than 11 but less than 39.

Edwin