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Chapter 4: Problem 66

Translate to an inequality. A number is greater than or equal to \(4 .\)

Short Answer

Expert verified
The inequality is \( x \geq 4 \).

Step by step solution

01

Identify the variable

Start by defining a variable to represent the unknown number. Let's use the variable \( x \).
02

Translate the phrase

The phrase 'greater than or equal to' is translated into the inequality symbol \( \geq \).
03

Write the inequality

Combine the variable from Step 1 and the symbol from Step 2 with the number given, which is 4. This forms the inequality \( x \geq 4 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Translating phrases to inequalities
In algebra, translating phrases to inequalities is an essential skill. It allows us to represent real-world scenarios mathematically. For example, consider the phrase 'A number is greater than or equal to 4.' To translate this, we follow these steps:

  • Identify the number or quantity involved. Here, it's 'a number'.
  • Recognize the relationship described by the phrase. The phrase says 'greater than or equal to'.
  • Connect the number and the relationship with an inequality. We use a variable to represent the unknown number, often 'x'.
By translating the phrase, we convert it into a mathematical inequality: \(x \geq 4 \). This process makes the relationships clear and easier to solve.
Inequality symbols
Inequality symbols are crucial in expressing mathematical relationships. They tell us how one value compares to another. The symbol \( \geq \) means 'greater than or equal to'. Here are the main inequality symbols:

  • \( > \): Greater than
  • \( < \): Less than
  • \( \geq \): Greater than or equal to
  • \( \leq \): Less than or equal to
Using these symbols correctly is essential in forming accurate mathematical expressions. When we see 'greater than or equal to', we use \( \geq \). For 'less than or equal to', we use \( \leq \). Practice recognizing and using these symbols to become more confident in writing inequalities.
Defining variables
In algebra, defining variables is the first step in creating equations or inequalities. A variable is a symbol, often a letter, that represents an unknown number. For instance, in the inequality \( x \geq 4 \), 'x' is the variable.

To define a variable effectively, follow these steps:
  • Choose a letter that makes sense. Common choices are 'x' or 'y'.
  • State clearly what the variable represents. For example, 'let x represent the number'.
  • Use the variable consistently throughout the problem.
Defining variables clearly helps keep your work organized and makes it easier to solve problems. It's a fundamental skill in algebra that paves the way for solving more complex equations and inequalities.

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Most popular questions from this chapter

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