Final answer:
Inequalities can be written in different forms by performing equivalent operations, like dividing or subtracting the same amount from both sides, and they still represent the same relationship. They can also be graphically represented, for example, on a number line or through the use of a Lorenz Curve in the context of income distribution.
Step-by-step explanation:
Inequalities can represent relationships between numbers or variables in different ways while still maintaining the same meaning. For instance, if we have the inequality 2x > 10, we can divide both sides by 2 to get x > 5. Both inequalities convey that x is a number greater than 5, but they are written differently.
Another way to express the same relationship could be by subtracting a number from both sides, for example, subtracting 2 from both sides of x > 5 yields x - 2 > 3, which still keeps the relationship between x and the number 3 the same.
Inequalities can also be represented graphically, such as with a number line. Mapping x > 5 on a number line would involve a ray starting just after the number 5 and extending infinitely to the right, indicating all the numbers greater than 5.
Understanding that inequalities can be modified without changing their meaning is crucial for various mathematical tasks, including solving algebraic equations and representing data like income distribution graphically, which can be done using a Lorenz Curve or other types of graphs like bar graphs, line graphs, or pie charts.