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Concept

Solution Set of an Inequality

Inequalities compare two quantities and often involve one or more variables. A solution of an inequality is any value of the variable that makes the inequality true. As an example, consider the following inequality.
Notice that if is substituted for in the inequality, the inequality holds true. Therefore, it can be said that is a solution to the given inequality.
However, this is not the only value that makes the inequality true. There are other values like and that make it true. The set of all possible values that satisfy an inequality is the solution set of an inequality. The solution set can be determined by applying the Properties of Inequalities to isolate the variable on one side of the inequality.
Solve for
Lastly, the solution set of the inequality can be represented using set-builder notation.
It is worth noting that the solution set of a linear inequality in one variable can also be represented using a number line.