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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: \( T \leq -3 \)

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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.

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