Problem 32 Use either $<$ or $>$ ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 32

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

Short Answer

Expert verified

-3 > -4

Step by step solution

- Identify the numbers

The numbers given in the inequality are (-3) and (-4).

- Understand the concept

For negative numbers, the number which is closer to zero is always greater because it is less negative.

- Compare the numbers

Between -3 and -4, (-3) is greater than (-4) because (-3) is closer to zero compared to (-4).

- Select the correct inequality

Since (-3) is greater than (-4), we write (-3 > -4).

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Key Concepts

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

Inequality Symbols

In mathematics, we use inequality symbols to compare numbers and show their relative sizes. The main inequality symbols are:

<: less than
>: greater than

When we compare two numbers, we place the appropriate symbol between them. The pointed end of the symbol faces the smaller number, and the open end faces the larger number. For example, in the statement $ 2 > 1 $, 2 is greater than 1, so the open end faces 2 and the pointed end faces 1. Inequality symbols help us express relationships clearly and accurately.

Negative Number Properties

Negative numbers have unique properties that often confuse students. A key property to remember is:

As numbers get more negative, they decrease in value.

For example, -1 is greater than -2 because -1 is closer to zero and therefore less negative. This might seem confusing at first because -2 is 'bigger' than -1 when we think of their absolute values, but in terms of value on the number line, -1 is actually greater than -2. Always remember, less negative means closer to zero! So anytime you encounter negative numbers in an inequality, think about their proximity to zero.

Number Line Comparison

A number line is a great visual tool to compare negative numbers. Imagine a horizontal line with zero at the center. Positive numbers are to the right of zero, and negative numbers are to the left. When comparing negative numbers like -3 and -4, locate them on the number line:

-3 is to the right of -4.

This means -3 is greater than -4 because it is closer to zero. Using a number line helps you quickly see which numbers are greater or smaller, making comparisons much easier. Always remember: further left means more negative, and further right means less negative or positive.

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91影视

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

Short Answer

Step by step solution

- Identify the numbers

- Understand the concept

- Compare the numbers

- Select the correct inequality

Key Concepts

Inequality Symbols

Negative Number Properties

Number Line Comparison

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