6.1 Introduction

Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.  In general, inequalities can be either numerical inequality or algebraic inequality or a combination of both. Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.

The five symbols that are used to represent the linear inequalities are listed below:

\(
\begin{array}{|l|l|l|}
\hline \text { Symbol Name } & \text { Symbol } & \text { Example } \\
\hline \text { Not equal } & \neq & x \neq 5 \\
\hline \text { Less than } & (<) & x+7<\sqrt{3} \\
\hline \text { Greater than } & (>) & 1+10 x>2+16 x \\
\hline \text { Less than or equal to } & (\leq) & y \leq 4 \\
\hline \text { Greater than or equal to} & (\geq) & -3-\sqrt{3} x \geq 10 \\
\hline
\end{array}
\)