Problem 76 - Elementary Algebra

Question

Translate the following into a mathematical statement. Four is greater than or equal to negative twenty-one.

Step-by-Step Solution

Answer

\( 4 \geq -21 \)

Step 1: Identify Keywords

First, identify key terms in the problem statement. Here, 'four', 'greater than or equal to', and 'negative twenty-one' are crucial.

Step 2: Translate Numbers into Symbols

Convert the words 'four' and 'negative twenty-one' into their numeric representations. Thus, 'four' becomes 4 and 'negative twenty-one' becomes -21.

Step 3: Understand the Inequality

Recognize that 'greater than or equal to' is represented by the symbol \( \geq \) in mathematics.

Step 4: Write the Mathematical Statement

Combine the translated expressions into a mathematical inequality: \( 4 \geq -21 \).

Key Concepts

Mathematical Statement

A mathematical statement is a precise description or expression of a problem or fact using mathematical symbols and numbers. It provides a clear way of conveying information numerically, eliminating the ambiguity often found in worded descriptions. In the given exercise, translating the sentence "Four is greater than or equal to negative twenty-one" into numbers and symbols forms the mathematical statement. This process involves identifying the numbers involved and the relationship between them. Utilizing symbols like numbers and inequality signs helps in clearly understanding complex word problems. Transforming such sentences into mathematical statements ensures clarity and enables the application of mathematical operations and analysis.

Inequality Symbols

Inequality symbols are crucial in constructing mathematical statements that express relationships between values that are not equal. These include

• "Less than" (<),
• "Greater than" (>),
• "Less than or equal to" (\( \leq \)),
• "Greater than or equal to" (\( \geq \)), and
• "Not equal to" (≠).

These symbols indicate the kind of comparison being made, whether it’s about values being less or more, or equally possible. In the specific exercise, the keyword identified is "greater than or equal to", represented by the symbol \( \geq \). This symbol suggests that the first number, 4, is either greater than or at least equal to the second number, -21. Understanding these symbols is essential for correctly interpreting and solving inequalities.

Translating Words into Symbols

Translating words into symbols involves converting verbal phrases into mathematical expressions using numbers and symbols. This translation is fundamental in forming mathematical statements accurately.To translate, follow these steps:

• Identify and note down the numbers involved. In the exercise: 'four' to 4 and 'negative twenty-one' to -21.
• Determine the relational phrase: Here, "greater than or equal to." This involves choosing the correct inequality symbol, \( \geq \), reflecting this relationship.
• Combine these elements into a clear, cohesive mathematical statement that reflects the original word statement: \( 4 \geq -21 \).

Mastering this skill is crucial for solving and understanding many mathematical problems where verbal descriptions need to be tackled numerically.