/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Graph each set of real numbers o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 6

Graph each set of real numbers on a number line. \(\\{x \mid x \geq-5\\}\)

Short Answer

Expert verified
The graph of the set of numbers \(x \geq -5\) on a number line starts from -5 (inclusive) and extends indefinitely to the right.

Step by step solution

01

Understanding the inequality

The inequality \(x \geq -5\) means that \(x\) is any number greater than or equal to -5. This includes -5 itself and all numbers to the right of -5 on a number line.
02

Preparing the number line

Before graphing, prepare a number line. The number line should have -5 marked as well as a few numbers to the right and left of -5 for reference.
03

Graphing the set of numbers

Begin graphing the set of numbers by shading in -5. Then, shade in all numbers to the right of -5 to represent the set of numbers greater than -5. This visually represents all solutions to the inequality.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Inequalities
Inequalities are mathematical expressions used to show that one quantity is less than or greater than another. Unlike equations, which show exact values, inequalities describe a range of possible values. They are expressed using symbols such as:
  • ">" which means 'greater than'
  • "<" which means 'less than'
  • "鈮�" which means 'greater than or equal to'
  • "鈮�" which means 'less than or equal to'
In the given problem, the inequality is written as \(x \geq -5\). This indicates that the solution includes not just one number but a continuum of numbers starting at -5 and extending towards infinity on the positive side of a number line. Understanding the inequality is the first step in visualizing a range of values on a number line.
Exploring Real Numbers
Real numbers encompass all the numbers that exist along the number line. This means they include both rational and irrational numbers.
  • Rational numbers are numbers that can be expressed as fractions, like 1/2, 0.75, or -2. They include integers such as -5, -4, 0, and 3.
  • Irrational numbers cannot be expressed exactly as fractions. Examples include square roots of non-perfect squares, such as \(\sqrt{2}\), and numbers like \(\pi\).
Within the context of graphing inequalities, understanding real numbers is important. In the expression \(x \geq -5\), \(x\) represents real numbers. This implies the solution is not limited to whole numbers but includes fractions and decimals, such as -4.8 or 0.1, as long as they are greater than or equal to -5.
Graphing Solutions on a Number Line
Graphing solutions on a number line is a visual way to represent solutions to inequalities. Here's how we can graph the inequality \(x \geq -5\):
  • First, draw a straight line and mark a few reference points including -5 on this line.
  • Next, indicate that -5 is included in the solution by either coloring or shading the point directly at -5. For more clarity, draw a filled dot over -5.
  • Then, continue shading towards the right side of the number line, covering all values greater than -5. This shaded area indicates all possible solutions to the inequality.
By following these steps, you create a clear visual representation that quickly conveys the solution set. This method is essential for understanding which numbers satisfy the inequality and for communicating it to others effectively.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the quadratic equations in Exercises 37-52 by factoring. \(x^{2}-12 x=-36\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+5 x+2=0\)

Factor the trinomials or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+17 x+16\)

Solve each equation by the method of your choice. \((2 x-6)(x+2)=5(x-1)-12\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(3 x^{2}=5 x-1\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.