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Chapter 0: Problem 42

Write each statement as an inequality. \(b\) is at most -6.

Short Answer

Expert verified
b \leq -6

Step by step solution

01

Understanding the Phrase

The key phrase here is 'at most'. This means the value of \(b\) cannot be greater than -6.
02

Choosing the Inequality Symbol

Since \(b\) cannot be greater than -6, the appropriate inequality symbol is \(\leq\).
03

Writing the Inequality

Combine the variable, the symbol, and the number to form the inequality. This yields \[ b \leq -6 \].

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Key Concepts

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

writing inequalities
When we talk about writing inequalities, we're referring to expressing relationships where one quantity is not equal to another in terms of being greater or smaller. Understanding the language and phrases used is key. For example, 'at most' means that the value we're discussing cannot exceed a certain number. If we say a variable is 'at most -6', this means the highest possible value is -6. It can be equal to -6 or any number smaller than -6. To write this as an inequality, we identify the variable (in this case, \( b \)), pair it with the correct inequality symbol (discussed below), and then add the number (\( -6 \)).
inequality symbols
Inequality symbols help us compare values. Here are the main ones:
  • \( \text{<} \): less than
  • \( \text{>} \): greater than
  • \( \text{\textless\textasciitilde} \): less than or equal to
  • \( \text{>\textasciitilde} \): greater than or equal to
In our example, the phrase 'at most' indicates that the value should not exceed a particular number, so we need to use \( \text{\textless\textasciitilde} \). This symbol tells us that the variable is either less than or equal to a certain value. Applying it, we get \( b \text{\textless\textasciitilde} -6 \).
algebraic expressions
Algebraic expressions combine numbers, variables, and operations. Here, we use the variable \( b \) to represent an unknown quantity. By writing inequalities, we are creating an algebraic expression that shows the relationship between \( b \) and the number \( -6 \).
The expression \( b \text{\textless\textasciitilde} -6 \) includes:
  • A variable \( (b) \)
  • An inequality symbol \( (\text{\textless\textasciitilde}) \)
  • A number \( (-6) \)
These elements together form an inequality that communicates the restriction placed on \( b \). So, whenever you encounter phrases like 'at most' or 'no more than', you now know how to translate them into a precise algebraic expression.

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Most popular questions from this chapter

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