In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the equivalent form cx[superscript 2] + dx + e < Ax + B most of the college algebra text books use either the sign chart for the left-hand side of the first inequality or graphs both functions which appear in each side of the second inequality (e.g., Swokowski & Jeffery, 2000). In both approaches the solution is rather long. Some text books, for example Sullivan (2012), simplify the graphing approach to picture the graph of the quadratic function, locate the real zeros, if any, decide whether the graph of the function lies above or below the real line (x-axis) and finally obtain the interval solution of the first inequality. In this article, we present an algebraic approach to solve the above quadratic inequality. The proof can be taught to the students using algebraic results introduced earlier in the course. The approach and its proof do not use the sign chart, graphing functions or the simplified graphing approach as mentioned above.