"determine the minimum and maximum limits for each missing side length in the triangles below"pls i really don't get what they want me to do.

Part A

Let,
m = missing side of the triangle

It turns out by the triangle inequality theorem that if we know two sides of a triangle, then the third side m is constrained by the compound inequality:
b-a < m < b+a
The value of b is larger than 'a'; unless a = b.

In this case, a = 13 and b = 19 are the two known sides, so...
b-a < m < b+a
19-13 < m < 19+13
6 < m < 32

The missing side length is between 6 and 32 units. 
The missing side length cannot be 6 units long, or else a triangle won't form (we'll get a straight line instead)
The missing side length cannot be 32 units long, or else a triangle won't form (we'll get a straight line instead) 


Part B

Same thing as before but now a = 14 and b = 15

m = missing side

b-a < m < b+a
15-14 < m < 15+14
1 < m < 29

The missing side length is between 1 and 29 units. 
The missing side length cannot be 1 unit long, or else a triangle won't form (we'll get a straight line instead)
The missing side length cannot be 29 units long, or else a triangle won't form (we'll get a straight line instead) 


Part C

a & b aren't known numerically so we just leave it as 

b-a < m < b+a

The missing side m is between b-a units and b+a units

m cannot equal b-a or else we'll form a straight line (and not a triangle)
m cannot equal b+a or else we'll form a straight line (and not a triangle)

1. 20-5x > -10

2. x < 6

Step-by-step explanation: