/*! 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 26 Graph on a plane. $$ x \geq ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 26

Graph on a plane. $$ x \geq 3 $$

Short Answer

Expert verified
Draw a solid vertical line at \( x = 3 \) and shade to the right.

Step by step solution

01

Understand the Inequality

The inequality is given as \( x \geq 3 \). This means that you need to graph all values of \( x \) that are greater than or equal to 3.
02

Draw the Boundary Line

Since the inequality includes \( x = 3 \), draw a vertical solid line at \( x = 3 \). The solid line indicates that points on the line are included in the solution.
03

Shade the Appropriate Region

Shade the region to the right of the line \( x = 3 \), as this represents all values of \( x \) that are greater than or equal to 3.
04

Verify the Solution

Pick a test point to the right side of the boundary line, such as \( x = 4 \). Check if it satisfies the inequality \( x \geq 3 \). Since 4 is greater than or equal to 3, the shading is correct.

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.

Coordinate Plane
The coordinate plane is a two-dimensional surface where we can plot points, lines, and regions. It's divided into four quadrants by the x-axis (horizontal axis) and the y-axis (vertical axis). Each point on the plane is designated by an ordered pair \( (x, y) \). The coordinate plane helps us visually represent mathematical equations and inequalities, making them easier to understand and solve. When we work with inequalities on the coordinate plane, we're looking at a specific region that satisfies the inequality's condition.
Boundary Line
The boundary line is a key component when graphing inequalities. It represents the values that exactly satisfy the equality part of the inequality. In our example, the inequality is \( x \geq 3 \). This means that the boundary line is at x = 3. To properly represent this in a graph, draw a vertical line at x = 3. Because our inequality includes \( \geq \), we use a solid line, indicating that points on the line (where x = 3) are included in the solution.
Shading Region
Shading the appropriate region is essential to properly represent an inequality on the coordinate plane. Once the boundary line is drawn, you need to determine which side of the line contains the solutions to the inequality. For the inequality \( x \geq 3 \), you shade the entire region to the right of the line x = 3. This indicates that all these points have x-coordinates that are greater than or equal to 3. Using shading helps to easily see which areas of the plane satisfy the inequality.
Inequality Representation
Inequality representation in graphing requires understanding both the boundary line and the shading region. We start by analyzing the given inequality, such as \( x \geq 3 \), to figure out what values it includes. Then, we draw the boundary line (solid or dashed depending on whether it is \( \geq \) or \( \gt \)). Next, shading the correct region of the coordinate plane visually represents all the possible solutions. Remember, inequality representation is all about accurately showing which points satisfy the given condition.

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 and graph. Write the answer using both set-builder notation and interval notation. $$ |x-3|+2>7 $$

Explain why the inequality \(|x+5| \geq 2\) can be interpreted as "the number \(x\) is at least 2 units from \(-5 . "\)

Graduate-School Admissions. Students entering a master's degree program at the University of Louisiana at Lafayette must meet minimum score requirements on the Graduate Records Examination (GRE). The GRE Verbal score must be at least 145 and the sum of the GRE Quantitative and Verbal scores must be at least \(287 .\) Each score has a maximum of \(170 .\) Using \(q\) for the quantitative score and \(v\) for the verbal score, write and graph a system of inequalities that represents all combinations that meet the requirements for entrance into the program.

Solve and graph. Write the answer using both set-builder notation and interval notation. Let \(f(x)=|2 x-3| .\) Find all \(x\) for which \(f(x) \leq 4\)

Luggage Size . Unless an additional fee is paid, some major airlines will not check any luggage for which the sum of the item's length, width, and height exceeds 62 in. The U.S. Postal Service will ship a package only if the sum of the package's length and girth (distance around its midsection) does not exceed 130 in. Video Promotions is ordering several \(30-\) in. long cases that will be both mailed and checked as luggage. Using \(w\) and \(h\) for width and height (in inches), respectively, write and graph an inequality that represents all acceptable combinations of width and height.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

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.