Problem 3 - Prealgebra

Question

More than 8000 fans attended the Wizards' opening soccer game at Arrowhead Stadium in Kansas City, Missouri. Write an inequality to describe the attendance.

Step-by-Step Solution

Answer

The inequality is \( x > 8000 \).

Step 1: Understand the Problem

The problem requires us to describe attendance with an inequality. Specifically, we need to show that attendance was more than 8000 fans.

Step 2: Define Variables

Let the variable \( x \) represent the number of fans who attended the game.

Step 3: Set Up the Inequality

Since the attendance was more than 8000, the inequality can be set as: \( x > 8000 \).

Step 4: Interpret the Inequality

This inequality states that the number of fans \( x \) is greater than 8000, representing that attendance exceeded 8000.

Key Concepts

Understanding Variables

Variables are essential components in mathematics. They act as placeholders or symbols that can represent different values. In this context, a variable is used to describe the number of fans who attended the soccer game. Variables are typically represented by letters from the alphabet such as \( x \), \( y \), or \( z \). This allows for a flexible representation of numbers.
In our exercise, the variable \( x \) stands for the number of attendees. It's crucial to define the variable clearly so that anyone reading the inequality can understand what is being represented. By using variables, we can express complex mathematical ideas simply and solve equations more effectively.

Solving Inequality Problems

Inequality problems involve mathematical statements that compare different quantities. Unlike equations, inequalities show relationships using symbols like \( > \), \( < \), \( \geq \), or \( \leq \). These symbols mean "greater than," "less than," "greater than or equal to," and "less than or equal to," respectively.
In this example, we aim to express that the number of fans is more than 8000. Inequality problems often require us to decide which direction the inequality sign should face. In our case, \( x > 8000 \) indicates that the attendance exceeded 8000. This clarification helps us understand the relationship between our variable \( x \) and the specific figure given in the problem. Practicing inequality problems helps improve skills needed to assess quantitative comparisons.

Expressing Mathematical Expressions

Mathematical expressions are composed of numbers, variables, operations, and sometimes inequalities or equalities. They form the building blocks of statements that describe relationships between quantities.
Creating expressions from verbal descriptions requires understanding of key terms and their mathematical counterparts. For example, "more than 8000" in our math problem translates to the inequality \( x > 8000 \). This transformation is a vital skill when translating real-world situations into mathematical language.

• An expression like \( x > 8000 \) consists of a variable \( x \), an inequality symbol \( > \), and the number \( 8000 \).
• Each component of the expression plays a crucial role in conveying meaning.

Understanding how to create and manipulate these expressions is an essential part of mastering math concepts. It allows problem solvers to succinctly represent diverse scenarios and solve various types of math problems.