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Chapter 2: Problem 8

For exercises 1-8, use a number line graph to represent the inequality. $$ -7

Short Answer

Expert verified
Draw an open circle at -7 on a number line and a line extending to the right.

Step by step solution

01

Understand the Inequality

The inequality given is -7 < x This means that x is greater than -7.
02

Draw a Number Line

Draw a horizontal line and mark even intervals on it. Label the central point as -7 and include other numbers such as -6, -5, -8, -9, etc., for context.
03

Represent the Inequality

To represent -7 < x place an open circle (not filled in) at -7 to indicate that -7 is not included. Then, draw a line extending to the right from -7 to show that x includes all values greater than -7.

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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 horizontal line that shows numbers at uniform distances. It's a visual way to represent values and their relationships.

When drawing a number line, follow these steps:
  • Start by drawing a straight, horizontal line.
  • Mark evenly spaced tick marks along the line.
  • Label these marks with numbers in increasing order from left to right.
For this particular exercise, ensure you label the number at the center around which the inequality revolves. This helps in clear visualization. In the given exercise, -7 should be the central reference point. Numbers like -8, -6, -5 etc., should be placed around it to provide context.
open circle
An open circle is often used on a number line to represent that a specific number is not included in a range. This is especially useful when dealing with inequalities.

Here鈥檚 how to use an open circle for the given inequality -7 < x:
  • Draw a small circle at -7. Do not fill it in. The open circle indicates that the value of -7 is not included in the solution set.
  • From the open circle, draw a line extending to the right. This visualizes that x takes all values greater than -7 but not -7 itself.
This clear visual representation helps to avoid confusion, making it obvious which values are part of the inequality.
greater than
The concept of 'greater than' (>) indicates that one number is larger than another. For the exercise -7 < x, it translates to x being any number larger than -7.

Here鈥檚 how to represent 'greater than' on a number line:
  • Once you have your open circle at -7, extend a line from the circle to the right.
  • This line shows that x can take any value more than -7.
  • No part of this line should include -7, so the circle remains open to represent this.
Understanding '<' or '>' is crucial, as it tells us whether a value is included or excluded, and whether the range extends left or right from the given point. For -7 < x, we always extend to the right on the number line, showing all values greater than -7.

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Most popular questions from this chapter

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