Two sides of a triangle have lengths 6 and 16. Which inequalities represent the possible lengths for the third side, x?

let a,b, and c be the lengths of the three sides of a triangle

there are three inequalities:

a+b>c

a+c>b

b+c>a

for your lengths, let a=16 and b=6, therefore a+b>c or 16+6>c; so 22>c or c<22

c can be how much less than 22 ?

look at b+c>a, 6+c>16, c>10

therefore c can be in the following range: 10<c<22