Problem 12 - Contemporary Precalculus

Question

Express the given statement in symbols. -17 is less than 6

Step-by-Step Solution

Answer

Question: Express the statement "-17 is less than 6" using mathematical symbols. Answer: -17 < 6

Step 1: Identify the numbers involved in the statement

The numbers involved in the statement are -17 and 6.

Step 2: Identify the relationship between the numbers

The relationship between the numbers is that -17 is less than 6.

Step 3: Express the relationship using symbols

Use the less than symbol ("<") to express the relationship between -17 and 6. This can be written as: -17 < 6

Key Concepts

Inequality Symbols

Inequality symbols allow us to express the relationship between two values where they are not equal. These symbols are essential in mathematics, providing a concise way to communicate expressions involving comparisons. Common inequality symbols include:

• "<": less than
• ">": greater than
• "≤": less than or equal to
• "≥": greater than or equal to

In the given exercise, the statement "-17 is less than 6" utilizes the symbol "<" to express the inequality.
By using this symbol, we can quickly convey that -17 is placed to the left of 6 on a number line, indicating a smaller value. Mastering these symbols boosts your ability to read and write mathematical statements efficiently.

Mathematical Notation

Mathematical notation is the language through which we communicate complex ideas simply and universally. In mathematics, notation refers to a system of symbols and signs that represent numbers, operations, relationships, and more.
The use of symbols, as seen in expressing inequalities, is a part of mathematical notation.
It allows for the translation of verbal statements into concise mathematical language, making it easier to solve problems and understand relationships.
The given statement "-17 is less than 6" is not only simpler once written using the notation as "-17 < 6," but also serves to eliminate ambiguity. Understanding mathematical notation is crucial for students to excel in higher-level math, where precision and clarity are of utmost importance.

Problem Solving Skills

Problem-solving skills are integral to success in mathematics and beyond. They involve the ability to identify what is being asked, analyze information, and apply logical methods to reach a solution.
In this exercise, identifying the numbers and their relationship is a key step in translating the verbal statement into mathematical symbols.
This methodical approach nurtures critical thinking, as students must:

• Recognize and extract relevant information
• Understand the relationship between elements
• Convert relationships into mathematical statements using appropriate symbols

Fostering these skills empowers students to tackle various mathematical challenges confidently. By practicing with simple problems like the one in the exercise, students build a strong foundation for solving more complex equations and inequalities.