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Chapter 1: Problem 25

Write the meaning of each inequality, and determine whether it is a true statement. $$ -9>1 $$

Short Answer

Expert verified
'-9 > 1' means '-9 is greater than 1'. The statement is false.

Step by step solution

01

Understand the Inequality

The inequality given is -9 > 1. The symbol '>' means 'greater than.' So, -9 > 1 means '-9 is greater than 1'.
02

Analyze the Inequality

Now, compare the two numbers, -9 and 1. A negative number is always less than a positive number, hence -9 is less than 1.
03

Determine Truth Value

Since -9 is less than 1, the statement '-9 > 1' is false.

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Key Concepts

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

Inequality Symbols
Inequality symbols are used to compare values and express the relationship between them. The main symbols include:

  • Greater than (>): Indicates that the value on the left is larger than the value on the right.
  • Less than (<): Indicates that the value on the left is smaller than the value on the right.
  • Greater than or equal to (鈮�): Indicates that the value on the left is either larger than or equal to the value on the right.
  • Less than or equal to (鈮�): Indicates that the value on the left is either smaller than or equal to the value on the right.
  • Not equal to (鈮�): Indicates that the two values are not the same.

In our exercise, the inequality symbol used is '>'. This means we need to check if the number on the left is larger than the number on the right.
Comparing Numbers
Comparing numbers is a fundamental skill in algebra. To compare numbers, you need to understand both positive and negative values.

  • Positive Numbers: Numbers greater than zero, such as 1, 2, and 3, are considered positive.
  • Negative Numbers: Numbers less than zero, such as -1, -2, and -3, are considered negative.

Negative numbers are always less than positive numbers. For instance, -9 is less than 1. When comparing -9 and 1, -9 is further to the left on the number line than 1, indicating it is smaller.

In our exercise, we compare -9 and 1. Since -9 is a negative number and 1 is a positive number, -9 is always less than 1.
Truth Value of Inequalities
The truth value of an inequality determines whether the inequality statement is true or false. You achieve this by comparing the values on both sides of the inequality symbol.

  • For example, in the inequality -9 > 1, we need to check if -9 is greater than 1.
  • As discussed, -9 is less than 1 since it is a negative number and 1 is positive.

Since -9 is not greater than 1, the statement '-9 > 1' is false. Understanding truth values is essential for solving and verifying inequalities correctly.

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