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Chapter 15: Problem 5

Classify each equation or inequality as true or false. $$ 0>-5 $$

Short Answer

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Step by step solution

01

Understand the Inequality

The inequality presented is \(0 > -5\). This means we need to determine whether 0 is greater than -5 on the number line.
02

Analyze the Numbers

Consider the positions of the numbers on the number line. Number 0 is to the right of -5, meaning 0 is greater than -5.
03

Conclude the Comparison

Since 0 is to the right of -5 on the number line, the inequality \(0 > -5\) is true.

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Key Concepts

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

inequalities
Inequalities are mathematical expressions that compare two values. Instead of saying something is equal to another, inequalities tell us if one value is larger, smaller, or between two other values. In this exercise, we are given the inequality \(0 > -5\). It uses the 'greater than' symbol (\(>\)). Inequalities are fundamental in mathematics as they help show relationships between numbers and variables in a clear way. There are several inequality symbols:
  • \(>\) means 'greater than.'
  • \(<\) means 'less than.'
  • \(\geq\) means 'greater than or equal to.'
  • \(\leq\) means 'less than or equal to.'
An inequality like \(0 > -5\) tells us that one number (here, 0) is larger than another (here, -5).
number line
When working with inequalities, the number line is very useful. The number line is a simple yet powerful visual tool that helps us understand the relationship between numbers. Numbers to the left are smaller, and numbers to the right are larger. For instance, on the number line:
  • The number -5 is to the left of 0.
  • This means -5 is less than 0, and conversely, 0 is greater than -5.
Visualizing inequalities on the number line helps us see which numbers are larger or smaller. Whenever you're in doubt, drawing a simple number line for quick reference can clarify things instantly.
greater than
The 'greater than' symbol \(>\) is used to compare two numbers, where the number on the left is larger than the number on the right. For example, in the exercise given:
  • \(0 > -5\) means 0 is greater than -5.
We can verify this by checking their positions on the number line, where 0 is to the right of -5, confirming that 0 is indeed greater. Understanding the 'greater than' symbol is crucial as it is widely used in mathematics to establish the order and comparison between numbers. It's also important to note that a number is always greater than any number that is to its left on the number line.

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