/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Translate to an inequality. Th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 11

Translate to an inequality. The temperature is at most \(-3^{\circ} \mathrm{C}\)

Short Answer

Expert verified
The inequality is \( T \leq -3 \).

Step by step solution

01

Identify the Key Phrase

The key phrase in the problem is 'at most'. This means that the temperature cannot be more than \(-3^{\circ} \mathrm{C}\).
02

Determine the Inequality Symbol

Since 'at most' means less than or equal to, the appropriate inequality symbol to use is \(\leq\).
03

Introduce the Temperature Variable

Let \( T \) represent the temperature. The inequality will compare \( T \) to \(-3^{\circ} \mathrm{C}\).
04

Write the Inequality

Combine the inequality symbol with the variable and the given temperature: \( T \leq -3 \)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

temperature
Temperature is a measure of how hot or cold something is. In many math problems, temperature can be represented with a variable to make it easier to work with. For example, we might use the variable \(T\) to denote temperature.
So, if we're discussing a temperature being at most \(-3^{\circ} \mathrm{C}\), it means the temperature can be \(-3^{\circ} \mathrm{C}\) or any value lower than that.
This concept is important because it helps simplify real-world conditions into mathematical expressions that can be easily worked with.
inequality symbols
Inequality symbols are used to show the relationship between two values where they are not necessarily equal. They are critical in mathematical expressions to indicate limits or conditions.
Here are common inequality symbols and their meanings:
  • \(>\): Greater than
  • \(<\): Less than
  • \(\geq\): Greater than or equal to
  • \(\leq\): Less than or equal to

In our problem, we use \(T \leq -3\) to show that the temperature is at most \(-3^{\circ} \mathrm{C}\). The symbol \(\leq\) is chosen because 'at most' means the temperature cannot exceed \(-3^{\circ} \mathrm{C}\), although it can be exactly \(-3^{\circ} \mathrm{C}\) or lower.
variables in inequalities
A variable in an inequality represents an unknown value that can change or vary. We use variables to write inequalities in a flexible and general way.
For example, in the inequality \(T \leq -3\), the variable \(T\) stands for the actual temperature. This inequality tells us that whatever value \(T\) takes, it should be less than or equal to \(-3^{\circ} \mathrm{C}\).
When you use inequalities, variables allow you to express relationships and conditions clearly and concisely. They make it easier to understand and solve real-world problems mathematically.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Match the sentence with one of the following: $$ a

Use an inequality and the five-step process to solve each problem. To remain on financial aid, Millie must complete an average of at least 7 credits per quarter each year. In the first three quarters of \(2010,\) Millie completed \(5,7,\) and 8 credits. How many credits of course work must Millie complete in the fourth quarter if she is to remain on financial aid?

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

Use an inequality and the five-step process to solve each problem. Reduced Fat Oreo " cookies contain 4.5 of fat per serving. In order for a food to be labeled "reduced fat," it must have at least \(25 \%\) less fat than the regular item. What can you conclude about the number of grams of fat in a serving of the regular Oreo cookies?

Review operations with real numbers. Simplify. $$ 3-2+5 \cdot 10 \div 5^{2} \cdot 2 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.