we know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)
Based on this theorem, to be able to construct a triangle with three segments AB, BC and AC, the following inequalities must be fulfilled
1) [tex] AB+BC > AC [/tex]
2) [tex] BC+AC > AB [/tex]
3) [tex] AC+AB > BC [/tex]
With only one that is not fulfilled, the triangle can not be made
So
Analyze the options
option a) [tex] AC + AB > CB [/tex] ----->
is fulfilling the Triangle Inequality Theorem
option b) [tex] AC + CB < AB [/tex] ----->
is not fulfilling the Triangle Inequality Theorem
option c) [tex] AC + CB > AB [/tex] ----->
is fulfilling the Triangle Inequality Theorem
option d) [tex] AC + AB < CB [/tex] ----->
is not fulfilling the Triangle Inequality Theorem
therefore
the answer is
[tex] AC + CB < AB [/tex]
[tex] AC + AB < CB [/tex]
