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Chapter 1: Problem 43

Write a true sentence using either \(< or >\) $$ -6 \square 6 $$

Short Answer

Expert verified
The true sentence is -6 < 6.

Step by step solution

01

Understand the Symbols

The symbols '<' and '>' are used to compare two numbers. '<' means 'less than' and '>' means 'greater than'.
02

Identify the Numbers

Look at the numbers given in the problem. The first number is -6 and the second number is 6.
03

Compare the Numbers

Since -6 is on the left side of 0 on the number line and 6 is on the right side of 0, -6 is less than 6.
04

Choose the Correct Symbol

Since -6 is less than 6, the correct symbol to use is '<'.
05

Form the True Sentence

Combine the numbers with the correct symbol to form the true sentence: -6 < 6.

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Key Concepts

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

number line
A number line is a visual representation of numbers in a straight line. Each point on this line corresponds to a unique number.

It extends infinitely in both directions, with 0 usually placed at the center.

On a number line, numbers to the right of 0 are positive, while numbers to the left of 0 are negative. For example, -6 is to the left of 0, and 6 is to the right of 0.

This helps us visually see that -6 is indeed less than 6. Placing numbers on a number line is essential for understanding their relationships, such as which number is greater or lesser.
less than
The symbol '<' means 'less than.' It is used to compare two numbers and shows that the first number is smaller than the second. For example, in the sentence -6 < 6, the '<' symbol correctly indicates that -6 is less than 6.

To remember it easily, think of the '<' symbol like the mouth of a hungry alligator that always wants to eat the larger number. Thus, its open end points towards the bigger number.

Whenever you see '<,' it shows the first number is smaller. This makes it clear that -6 being less than 6 is a true statement.
greater than
The symbol '>' means 'greater than.' Like '<,' it is used to compare two numbers, but shows the opposite relationship 鈥� that the first number is bigger than the second.

For instance, if you compare 7 and 3, you would write 7 > 3. This indicates that 7 is greater than 3.

Just like the '<' symbol, you can remember '>' as the mouth of an alligator. This time, it opens towards the larger number, indicating that the first number is bigger.

Be attentive to these symbols; using the wrong one can lead to incorrect conclusions. In our exercise, -6 is not greater than 6, so we use -6 < 6 instead.

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Most popular questions from this chapter

Simplify. $$ 3 x^{2}+7-\left(2 x^{2}+5\right) $$

If \(n\) is positive and \(m\) is negative, what is the sign of \(n+(-m) ?\) Why?

Write an equivalent expression without using grouping symbols. $$ -[5 x-2 y-3 z] $$

A gambler loses a wager and then loses "double or nothing" (meaning the gambler owes twice as much) twice more. After the three losses, the gambler's assets are \(-\$ 20 .\) Explain how much the gambler originally bet and how the \(\$ 20\) debt occurred.

Evaluate. $$ \frac{a^{3}-4 a}{a(a-3)}, \text { for } a=-2 $$
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