One side of a triangle is 22 cm shorter than the base, x. the other side is 6 cm longer than the base. what lengths of the base will allow the perimeter of the triangle to be at least 31 cm

So, I believe x would have to be 23 at least for three reasons.
1. The side of a triangle can’t be a negative or a zero
2. 23-22, is 1(one side), x=23 (another side), 23+6, 29 (last side)
That is more than 31,
3. Anything less wouldn’t work because you have to have a number than is the same or bigger than x
So x = 23

8+9=17. Hope this help :)