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Chapter 1: Problem 66

Decide whether each statement is true or false. $$ -8>-2 $$

Short Answer

Expert verified
False

Step by step solution

01

Understand the Inequality

Analyze the given inequality ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline$$ -8 > -2 $$. This inequality compares the values of ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline -8 and -2. On the number line, numbers to the left are smaller and numbers to the right are larger.
02

Compare the Values

Identify the position of -8 and -2 on the number line. ewline ewlineewline ewline ewlineewline -8 is to the left of -2.ewline Therefore, -8 is smaller than -2.
03

Determine the Truth Value

Conclude that if -8 is smaller than -2, then the statement ewline ewlineewline~-8 > -2~ is false.

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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 visual tool used to compare and understand numbers in an easy way.
It is a horizontal line where numbers are placed at equal intervals.
The center of the number line is 0, with positive numbers to the right and negative numbers to the left.
Each position on the number line corresponds to a number.
For example, -8 is placed to the left of -2 on the number line.
This visual aid helps us quickly determine the relative size of numbers.
The farther a number is to the right, the larger it is. Conversely, the farther a number is to the left, the smaller it is.

Understanding and using the number line is essential in solving inequalities.
Comparing Values
Comparing values involves determining if one number is less than, greater than, or equal to another number.
In our exercise, we compared -8 and -2 using a number line.
Since -8 is to the left of -2, we know that -8 is smaller than -2.
To compare values effectively:
  • Use a number line as a reference.
  • Remember that numbers further to the left are smaller.
  • Numbers further to the right are larger.
Comparing values becomes straightforward
once you understand the basic rules and visualize them on a number line.
This will help you solve inequalities accurately.
Inequalities
Inequalities are statements about the relative values of two numbers.
They tell us if one number is less than (<), greater than (>), less than or equal to (鈮�), or greater than or equal to (鈮�) another number.
In the given inequality -8 > -2, we needed to determine if -8 is truly greater than -2.
By using the number line and comparing values, we saw that -8 is actually smaller than -2.
Therefore, the inequality -8 > -2 is false.
  • To work with inequalities, always visualize the numbers on a number line.
  • Compare their positions to find out which is larger or smaller.
  • Check if the inequality holds true based on your comparison.
Understanding inequalities is crucial in algebra as they are widely used
in various types of problems and applications.

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