Final answer:
The solutions to an inequality represent a range of values that satisfy the inequality condition, such as all values greater than or equal to -3 for r ≥ -3, whereas an equation like x = 2 has a single, precise solution. Inequalities reflect multiple possibilities, while equations define exact relationships.
Step-by-step explanation:
The primary difference between the solutions to an inequality and an equation lies in the nature of their solutions. For an inequality such as r ≥ -3, the solution is a range of values - specifically, all values of r that are greater than or equal to -3. In contrast, an equation like x = 2 has a single solution: the value of x must be exactly 2.
In terms of graphical representation, an inequality would be visualized on a number line with a range of values highlighted or on a coordinate plane with a shaded region. However, an equation is represented by a specific point on a number line or a line on a coordinate plane. Inequalities often arise in various contexts, such as when dealing with constraints in optimization problems or modeling scenarios with multiple possible outcomes. Equations are more directly used to find precise values or to describe exact relationships between variables.