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

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they 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.

Quadratic Functions

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

Graphing Solution Sets

Graphing solution sets involves representing the solutions of an inequality on a number line. This visual representation helps to easily identify the intervals that satisfy the inequality. When graphing, open circles are used for values that are not included in the solution (for < or >), while closed circles are used for values that are included (for ≤ or ≥). Understanding how to accurately graph these intervals is essential for interpreting the solution.