LINEAR INEQUALITY

An inequality is really just any mathematical statement relating two quantities using an inequality symbol such as <, >, ≤, or ≥. For solving inequalities that contain variable expressions, you may be asked to solve the inequality for that variable. This just means that you need to find the values of the variable that make the inequality true. Remember that when you solve a linear equation there is usually one value that makes the equation true. But when you solve an inequality, there can be many values that make the statement true!

Solving Linear Inequalities is very similar to solving equations. Instead of using the Properties of Equality, you use the Properties of Inequalities. These two sets of properties are almost identical except for one very, very important rule:

When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality symbol.

-->GRAPHING LINEAR INEQUALITY

Graphing inequalities is much easier than your book makes it look. Think about how you've done linear inequalities on the number line. For instance, you were asked to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing linear inequalities two-variable are very much the same.