Problem 71 Use $<$ or $>$ for \(\... [FREE SOLUTION]

91影视

Basic College Mathematics

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

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 71

Use $<$ or $>$ for $\square$ to write a true sentence. Draw the number line if necessary. $$ 0 \square 17 $$

Short Answer

Expert verified

0 < 17

Step by step solution

- Understand Inequality Symbols

Inequality symbols are used to compare two values. The symbol '<' means 'less than,' and the symbol '>' means 'greater than.' Your task is to determine whether 0 is less than or greater than 17.

- Compare the Numbers

Compare the values of 0 and 17. Since 0 comes before 17 on the number line, 0 is less than 17.

- Choose the Correct Symbol

Since you determined that 0 is less than 17, use the '<' symbol to complete the inequality: 0 < 17.

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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 straight line that has numbers placed at equal intervals or segments along its length. It is often used to represent numbers visually and to compare them more easily. You can imagine it as a ruler, but instead of measuring lengths, it measures values, both positive and negative. Here are some key points about number lines:

Number lines usually start with zero in the middle.
Positive numbers are placed to the right of zero.
Negative numbers are placed to the left of zero.

In our exercise, we compared 0 and 17. To draw a number line for this, you would place 0 at the center and 17 to its right. This visual helps you immediately see that 0 is less than 17 since it appears before (to the left of) 17. Number lines are handy tools for visually understanding the relationship between numbers.

comparing numbers

Comparing numbers means determining which number is greater, smaller, or if they are equal. To do this, you use inequality symbols like <, >, or =. Let's break this down:

'<' means 'less than.'
'>' means 'greater than.'
'=' means 'equal to.'

For example, when comparing 0 and 17, there are a few steps you can follow:

Visualize or draw a number line to see the position of the numbers.
Note that 0 is to the left of 17 on the number line.
Since 0 is to the left, it is less than 17, so we use the '<' symbol.

Therefore, the correct comparison is 0 < 17. This step-by-step approach helps ensure that you correctly determine the relationship between numbers.

less than and greater than symbols

Inequality symbols play a crucial role in mathematics for comparing two values. The '<' symbol means 'less than,' and the '>' symbol means 'greater than.' To use these symbols correctly:

'<' points to the smaller number (e.g., 5 < 10 means 5 is less than 10).
'>' points to the larger number (e.g., 10 > 5 means 10 is greater than 5).

Remember the alligator analogy often taught in schools: Imagine the symbol as an alligator's mouth that always wants to eat the bigger number. So, if you have 0 < 17, the alligator mouth opens towards 17, showing that it is the larger number. Similarly, if you had 17 > 0, the mouth would open towards 17. When comparing numbers, use these symbols to communicate clearly and accurately which number is larger or smaller.

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91影视

Use \(<\) or \(>\) for \(\square\) to write a true sentence. Draw the number line if necessary. $$ 0 \square 17 $$

Short Answer

Step by step solution

- Understand Inequality Symbols

- Compare the Numbers

- Choose the Correct Symbol

Key Concepts

number line

comparing numbers

less than and greater than symbols

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