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Chapter 4: Problem 76

Translate to an inequality. The number of volunteers was at most 20.

Short Answer

Expert verified
\( x \leq 20 \)

Step by step solution

01

Understand the Problem

Identify the key information given in the problem. The problem states that the number of volunteers was at most 20.
02

Define the Variable

Let鈥檚 define a variable to represent the number of volunteers. Let \( x \) represent the number of volunteers.
03

Translate the Statement to an Inequality

The phrase 'at most 20' means that the number of volunteers can be 20 or fewer. To express this as an inequality, write \( x \leq 20 \).

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Key Concepts

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

Defining Variables
In algebra, variables are symbols used to represent unknown values. They are essential because they allow us to generalize problems and solve them systematically.

Here, we need to translate a statement about the number of volunteers into mathematical language. We start by defining a variable to represent the number of volunteers. Let鈥檚 choose the variable \( x \).

By defining our variable, we make it possible to translate the given information into an algebraic expression. Whenever you face a problem involving an unknown quantity, deciding on a variable is typically your first step. This helps clarify what you are working with and where you are aiming to get.
Translating Statements to Inequalities
Translating statements into inequalities involves interpreting the language used and expressing it mathematically.

In our example, the problem says, 'the number of volunteers was at most 20.' We defined \( x \) to be the number of volunteers. Then, we interpret 'at most 20.'

'At most' means the value cannot exceed 20. Therefore, \( x \) can be equal to 20 or any value less than 20. We translate this into the inequality \( x \leq 20 \).

This step is crucial because understanding how to convert phrases into mathematical statements will help you solve many types of problems more effectively.
Understanding Inequality Symbols
Inequalities are expressions that show the relationship between two values where they are not necessarily equal. The most common inequality symbols are:

  • \( < \): Less than
  • \( \leq \): Less than or equal to
  • \( > \): Greater than
  • \( \geq \): Greater than or equal to


In our exercise, we use \( \leq \) because 'at most 20' includes the number 20 itself and all numbers less than 20. So, the inequality \( x \leq 20 \) accurately reflects the statement.

Mastering these symbols is fundamental in algebra. It enables you to express and solve a wide range of problems involving inequalities.

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Most popular questions from this chapter

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