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Chapter 1: Problem 26

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

Short Answer

Expert verified
-9 is less than 1. The statement \[-9 < 1\] is true.

Step by step solution

01

Understand the inequality

The inequality given is \[-9 < 1\]. This inequality states that -9 is less than 1.
02

Interpret the meaning

To understand the meaning of the inequality \[-9 < 1\], we can think of it in terms of the position of the numbers on a number line. On a number line, -9 is to the left of 1, indicating that -9 is indeed less than 1.
03

Determine if the statement is true

To determine if the statement is true, compare the two numbers directly. Since -9 is to the left of 1 on the number line, \[-9 < 1\] is a true statement.

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Key Concepts

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

number line interpretation
To understand inequalities, using a number line is very helpful. A number line visually represents numbers in increasing order from left to right. For example, let's consider the given inequality \(-9 < 1\). On a number line, \(-9\) will be placed to the left of \(1\). This left-to-right position indicates that \(-9\) is indeed less than \(1\). Drawing or visualizing a number line helps us quickly see the relationships between numbers and interpret inequalities easily.
less than comparison
Comparing two numbers to understand inequalities involves determining their relative positions. In the inequality \(-9 < 1\), the symbol \(<\) indicates that the number on the left is smaller than the number on the right. To determine if this is true, you compare their sizes directly. Because \(-9\) is farther left on the number line than \(1\), it is smaller. The 'less than' symbol \(<\) helps in identifying smaller values in comparison scenarios, and here, it confirms that \(-9\) is indeed less than \(1\).
true statement validation
To validate if an inequality statement is true, we need to assess the comparison made. For the inequality \(-9 < 1\), since \(-9\) is to the left of \(1\) on the number line, it is smaller, making the statement true. Always ensure the number on the left is indeed less than the number on the right for a 'less than' comparison. In summary, knowing how to validate inequalities helps confirm their truthfulness. Verifying that \(-9 < 1\) is true strengthens the understanding of number positions and comparisons on a number line.

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Most popular questions from this chapter

Find an equivalent expression by factoring. $$ 5 x+50 $$

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