In Exercises 53-62, some applications of inequalities are...

In Exercises $53-62,$ some applications of inequalities are shown. Fossils found in Jurassic rocks indicate that dinosaurs flourished during the Jurassic geological period, 140 MY (million years ago) to 200 MY. Write this as an inequality, with $t$ representing past time. Graph the values of $t$.

In Exercises $53-62,$ some applications of inequalities are shown.
Fossils found in Jurassic rocks indicate that dinosaurs flourished during the Jurassic geological period, 140 MY (million years ago) to 200 MY. Write this as an inequality, with $t$ representing past time. Graph the values of $t$.

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Key Concepts

Inequalities

Inequalities are mathematical tools used to represent relationships that are not strictly equal, indicating that one value is greater than, less than, or possibly equal to another. They are essential in problems where quantities fall within a certain range rather than a single value.

Interval Representation

Interval representation involves expressing a range of values that satisfy an inequality. This method allows for a clear description of all possible values a variable may take, which is fundamental in solving and visualizing inequalities.

Graphing on a Number Line

Graphing on a number line is a technique used to visually depict the set of solutions to an inequality. It involves marking endpoints, typically with open or closed circles to denote whether the endpoints are included, and shading the region representing all values that satisfy the inequality.

Translating Context to Mathematical Form

Translating real-world scenarios into mathematical expressions is a critical skill. This involves converting contextual information or data into mathematical inequalities or equations, which can then be analyzed and solved using established mathematical methods.

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