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Chapter 10: Problem 30

Use either \(<\) or \(>\) for \(\square\) to write a true sentence. $$ -4 \square-3 $$

Short Answer

Expert verified
-4 is less than -3, so -4 < -3.

Step by step solution

01

- Understand the Problem

The goal is to determine which inequality symbol (< or >) makes the statement true when comparing -4 and -3.
02

- Compare the Numbers

Recognize that on the number line, numbers to the left are smaller. Since -4 is to the left of -3, -4 is less than -3.
03

- Choose the Correct Symbol

Since -4 is less than -3, the symbol < (less than) should be used to make the sentence true.
04

- Write the True Sentence

Replace the square with the selected symbol to complete the true sentence: -4 < -3.

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Key Concepts

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

comparing numbers
When we compare numbers, we try to determine their order or relative size. This is especially important in mathematics for solving equations and understanding relationships between values. For instance, comparing -4 and -3 involves determining which number is smaller or larger when placed on a number line.

Small numbers (in terms of magnitude) are generally to the right on a number line, while larger numbers are on the left. Understanding this fundamental concept helps in solving many mathematical problems where comparison is required.
number line
A number line is a visual representation of numbers placed equally apart on a straight line. This helps us see the order and spacing of numbers clearly. It usually includes positive numbers, negative numbers, and zero.

On a number line:
  • Numbers to the right are greater.
  • Numbers to the left are smaller.
For example, -4 is to the left of -3, meaning -4 is less than -3. Number lines are particularly useful for visual learners and help simplify the process of comparing numbers and understanding their relationships.
less than symbol
The less than symbol \(<\) is used to show that one number is smaller than another. When you see \(-4 < -3\), it means that -4 is less than -3. This symbol helps to easily compare two numbers and state their relationship in a quick and clear way.

Remember:
  • The point of the \(<\) symbol always points to the smaller number.
  • Thus, reading \(-4 < -3\) can be thought of as '-4 is less than -3'.
This understanding is important for solving inequalities in mathematics and helps you interpret statements about numbers efficiently.
negative numbers
Negative numbers are numbers with a value less than zero. They are usually found to the left of zero on a number line. Comparing negative numbers can be tricky because a larger numerical value actually means a smaller quantity.

For example:
  • -4 is smaller than -3 because -4 is further to the left on the number line.
  • In essence, the more negative the number, the smaller its value.
Understanding how negative numbers work is crucial for mastering mathematics, as it comes up in various topics from basic arithmetic to advanced algebra.

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Most popular questions from this chapter

Simplify. $$ \begin{array}{l} 5^{3}+26 \cdot 71- \\ (16+25 \cdot 3) \end{array} $$

Multiply. \(9 \cdot(-2) \cdot(-6) \cdot 7\)

Divide. $$ \frac{-1.7}{20} $$

Solve. Stock Price. The price of a stock began the day at \(\$ 23.75\) per share and dropped \(\$ 1.38\) per hour for \(8 \mathrm{hr}\). What was the price of the stock after \(8 \mathrm{hr} ?\)

Multiply. \(-\frac{3}{5}\left(-\frac{2}{7}\right)\)
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