In Exercises 69–74, solve each inequality and graph the solution set on a real number line. 2x^2 + 5x - 3 < 0

Inequalities are mathematical statements that express the relationship between two expressions that are not equal. They use symbols such as <, >, ≤, and ≥ to indicate whether one side is less than, greater than, or equal to the other. Understanding how to manipulate and solve inequalities is crucial for determining the solution set of an inequality.

A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. Solving inequalities involving quadratic functions often requires finding the roots of the equation and analyzing the intervals between them.

Graphing solution sets involves representing the solutions of an inequality on a number line. This visual representation helps to easily identify the intervals where the inequality holds true. For quadratic inequalities, the graph typically includes open or closed circles to indicate whether endpoints are included in the solution set, based on the type of inequality used.