An inequality is a mathematical statement expressing that the quantities on both sides of the statement are not equal. Algebraically, these are those statements involving the symbols; <, >, \(\geq\) or \(\leq\). A single-variable inequality can be written in any of the following forms: \(x < C\), \(x > C\), \(x \leq C\) or \(x \geq C\), where \(C\) is any real numbers.
Solving linear inequality is similar to solving linear equations. To solve a single-variable inequality means to find all the numbers that would satisfy it. Unlike linear equations, linear inequalities have infinitely many solutions. So the graph of its solution set is a set all points, which is a subset of a line.
Before graphing linear inequalities, we summarized below the different forms of inequalities, with its corresponding interval form and graph:
Based on the table above, sketch the graph of the following inequalities: