Question

Which inequality can be used to explain why these three segments cannot be used to construct a triangle? AC + AB > CB AC + CB < AB AC + CB > AB AC + AB < CB

Answer 1

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) $AB+BC > AC$

2) $BC+AC > AB$

3) $AC+AB > BC$

With only one that is not fulfilled, the triangle can not be made

So

Analyze the options

option a) $AC + AB > CB$ -----> is fulfilling the Triangle Inequality Theorem

option b) $AC + CB < AB$ -----> is not fulfilling the Triangle Inequality Theorem

option c) $AC + CB > AB$ -----> is fulfilling the Triangle Inequality Theorem

option d) $AC + AB < CB$ -----> is not fulfilling the Triangle Inequality Theorem

therefore

the answer is

$AC + CB < AB$

$AC + AB < CB$

Answer 2

The answer is gonna have to be B.