Solution Set of an Inequality

A solution of an inequality is any value of the variable that makes the inequality true. If a value is substituted for the variable and creates a false statement, that value is not in a solution of the inequality. Consider the following inequality when x=-3, 0, and 3. 2x-3< 5 lcl 2( -3)-3? <5 & ⇒ & -9 < 5 ✓ [0.3em] 2( 0)-3? <5 & ⇒ & -3 < 5 ✓ [0.3em] 2( 3)-3? <5 & ⇒ & 6 ≮ 5 * The set of all possible values that satisfy an inequality is the solution set of an inequality. The solution set of the inequality can be represented using set-builder notation. \begin{gathered} \underline\textbf{Solution Set} \\ \{x\,|\,x\lt 4\} \end{gathered} The solution set of a linear inequality in one variable can also be represented using a number line.