Check the sign of the equation. If it is an equal sign, then the equation is a linear equation; if the equation contains <, >, ≤ or ≥, then it is a linear inequality. For example, if you check 4x+6 ≥ 22, then it is a linear inequality, as it contains a ≥ sign.
Look at the graphs of the linear equation and linear inequality. If the line is represented as a dashed line with a shaded region, it is the graph of a linear inequality. If the line is represented as a solid line, then it is the graph of a linear equation.
Plot the solutions of the equation on a number line. For linear inequalities that contain either a > or < sign in the mathematical expression, the line drawn on the number line will be a line with a parenthesis at the endpoint. But the representation of linear inequality containing either a ≥ or ≤ is a line with a square bracket at the endpoint. Parenthesis indicates that the endpoint is not included in the solution, whereas the square bracket shows that the endpoint is also included in the solution. For the linear equations, there will be a solid line drawn with arrow heads on both ends of the line.
Check the solution set of both the examples. If it has specific solutions, then it is a linear equation. If the solution set is a range of values, then it is a linear inequality. For example, if you solve 2x = 6, then the solution for x is 3, which is a specific value. This means that 2x = 6 is a linear equation. Consider the expression 2x < 6. The solution for this is x < 3, which means a range of values less than 3. This means that it is a linear inequality.