If c is an integer, then determine whether the statement $\left|x\right|+c<0$has no solution is sometimes, always or never true.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$will always be positive and hence the absolute value.

A number that is not fraction and whole in itself is called Integer. It includes positive and negative numbers along with 0.

If c is an integer, then $\left|x\right|+c<0$has no solution is sometimes true.

Check the validity

$\begin{array}{l}\left|x\right|+c<0\\ \left|x\right|+c-c<-c\\ \left|x\right|<-c\end{array}$

This inequality is true when c is a negative integer and this is false when c is a positive integer.

Hence, the statement $\left|x\right|+c<0$is sometimes true.