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Chapter 2: Problem 16

Translate to an inequality. Angenita earns no less than \(\$ 12\) per hour.

Short Answer

Expert verified
The inequality is \( h \geq 12 \).

Step by step solution

01

- Define the Variable

Let the variable \( h \) represent the number of dollars Angenita earns per hour.
02

- Understand the Phrase 'No Less Than'

The phrase 'no less than' means that the amount can be equal to or greater than a certain value.
03

- Translate the Phrase to an Inequality

Since Angenita earns no less than \( \$ 12 \) per hour, the inequality is: \[ h \geq 12 \]

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Key Concepts

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

Defining Variables
When solving problems in math, especially those involving inequalities, the first step is often defining the variables. In our example, we need to determine what we are measuring. The problem is about how much Angenita earns per hour, so we define a variable to represent this amount. Here, we choose h to represent the amount Angenita earns per hour. This process of defining variables is crucial for setting the foundation for the rest of the solution. Clear definitions make it easier to understand and solve the problem. It's like labeling different parts of a puzzle before putting it together.
Inequalities
Inequalities are mathematical statements that relate expressions that are not necessarily equal. They involve symbols like > (greater than), < (less than), 鈮� (greater than or equal to), and 鈮� (less than or equal to). In our example, we need an inequality to express that Angenita's hourly earnings are no less than \(12. This means her earnings can be equal to \)12 or greater. In mathematical terms, we write this as: \[ h \geq 12 \] where h represents her hourly earnings. The '鈮�' symbol is used because it allows for both possibilities: earning exactly $12 or more per hour.
Phrases in Inequalities
Translating phrases from everyday language into mathematical expressions is a key skill in solving inequalities. Core phrases such as 'no less than,' 'at least,' and 'maximum' often indicate the type of inequality you're dealing with. In our example, the phrase 'no less than' translates into the mathematical symbol '鈮�,' which conveys that the amount can be equal to or greater than a specific value. By understanding how these phrases work, you can more easily convert real-world problems into mathematical expressions. This process simplifies complex scenarios, making them easier to analyze and solve.

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Most popular questions from this chapter

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