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Chapter 3: Problem 76

Translate the given phrase or sentence algebraically. \(h\) is no less than \(8 .\)

Short Answer

Expert verified
The inequality is \( h \geq 8 \).

Step by step solution

01

Understand the Phrase

The phrase 'no less than' indicates a relationship where one quantity is greater than or equal to another quantity.
02

Identify Variables and Values

In the given phrase, the variable is denoted by \( h \) and the value is 8.
03

Set Up the Inequality

From the phrase, 'no less than' means that \( h \) must be greater than or equal to 8. This translates to the inequality \( h \geq 8 \).

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Key Concepts

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

Understanding Inequalities
Inequalities show the relationships between two values or expressions. Instead of stating that two quantities are exactly the same, inequalities indicate that one quantity is larger or smaller than the other. For example:
  • Greater than: represented as \( > \)
  • Less than: represented as \( < \)
  • Greater than or equal to: represented as \( \geq \)
  • Less than or equal to: represented as \( \leq \)
In the exercise, the phrase 'no less than' translates to the inequality symbol \( \geq \). This means that the variable in question is either greater than or equal to a certain number.
Introduction to Variables
Understanding variables is crucial in algebra. A variable represents an unknown value that can change or vary. It is typically denoted by letters such as \( x \), \( y \), or in this exercise, \( h \). Variables provide a way to generalize mathematical relationships and create equations or inequalities that apply to many situations. In the given exercise, the variable \( h \) helps us describe a range of possible values rather than a single solution.
Translating Phrases to Algebra
One of the foundational skills in algebra is translating verbal descriptions into mathematical expressions. This often involves identifying keywords or phrases and knowing what they represent. For example, phrases like 'no less than' or 'at least' suggest a relationship of \( \geq \), while phrases like 'no more than' or 'at most' suggest a relationship of \( \leq \).

Let's break down the exercise phrase 'no less than 8':
  • 'No less than' signals that our variable \( h \) is at least equal to or greater than the value 8.
  • Mathematically, we write this relationship as \( h \geq 8 \).
Thus, we've translated the verbal phrase into a precise algebraic inequality.

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Most popular questions from this chapter

An electrician charges \(\$ 45\) per hour for her time and \(\$ 24\) per hour for her assistant's time. On a certain job the assistant worked alone for 4 hours preparing the site, and then the electrician and her assistant completed the job together. If the total labor bill for the job was \(\$ 464,\) how many hours did the electrician work?

Translate the given phrase or sentence algebraically. \(y\) is no more than 2

Translate the given phrase or sentence algebraically. \(x\) is at least 5

Set up an inequality and solve it. Be sure to clearly label what the variable represents. If 9 less than 5 times a number is less than twice the number, how small must the number be?

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. How long will it take someone driving at 52 mph to travel 234 miles?
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