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Chapter 2: Problem 7

Determine whether inequality is true or false. \(-3<-9\)

Short Answer

Expert verified
The inequality \(-3 < -9\) is false.

Step by step solution

01

Understand the Inequality

The given inequality is \(-3 < -9\). This means checking if \(-3\) is less than \(-9\).
02

Evaluate Negative Numbers

Remember that on the number line, numbers to the left are smaller. For negative numbers, a smaller absolute value means it is larger. Compare \(-3\) and \(-9\).
03

Compare the Values

\(-3\) is to the right of \(-9\) on the number line. This means \(-3\) is actually greater than \(-9\), not less.
04

Determine the Truth Value

Since \(-3\) is not less than \(-9\), the inequality \(-3 < -9\) is false.

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Key Concepts

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

Negative Numbers
Negative numbers can be a bit tricky at first. They are the numbers less than zero and are usually denoted with a minus (-) sign. But the way we compare them is a bit different from positive numbers.
It's essential to remember that the closer a negative number is to zero, the larger it actually is. For example, \(-2\) is greater than \(-10\), even though 2 is less than 10 when they are positive numbers.
So, when comparing negative numbers, always think about which one is closer to zero to determine which is greater.
Number Line
Using a number line is super helpful in understanding inequalities, especially with negative numbers. Imagine a line where zero is in the middle. Numbers to the right of zero are positive, and those to the left are negative.
When positioned on the number line, the farther left a number is, the smaller it is. For example, on a number line, \(-9\) would be to the left of \(-3\), showing that \(-9\) is less than \(-3\).
This visual approach makes it easier to compare negative numbers and understand their order.
Truth Value of Inequalities
The truth value of an inequality tells us if a statement is true or false. In algebra, we often see statements like \(-3 < -9\).
To determine the truth value, we need to compare the numbers accurately. We've already learned that, on the number line, \(-3\) is to the right of \(-9\). This means \(-3\) is greater than \(-9\).
So, \(-3 < -9\) is a false statement. Understanding these concepts will help you confidently evaluate the truth value of any inequality in algebra.

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Most popular questions from this chapter

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