/*! 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 300 Graph each inequality on the num... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 300

Graph each inequality on the number line and write in interval notation. (a) \(-5

Short Answer

Expert verified
(a) \((-5, 2)\), (b) \([-3, 1)\), (c) \[0, 1.5\].

Step by step solution

01

- Graph the inequality for (a)

To graph \(-5 < x < 2\) on a number line:1. Draw a number line with numbers including -5 and 2.2. Use an open circle at -5 to show that -5 is not included in the solution.3. Draw another open circle at 2 to show that 2 is not included either.4. Shade the region between -5 and 2 to indicate all numbers between these points are solutions.
02

- Write (a) in interval notation

In interval notation, represent the region from the graph where all x values are solutions:Therefore, the interval notation is \((-5, 2)\).
03

- Graph the inequality for (b)

To graph \(-3 \leq x < 1\) on a number line:1. Draw a number line with numbers including -3 and 1.2. Use a closed circle at -3 to show that -3 is included in the solution.3. Draw an open circle at 1 to show that 1 is not included.4. Shade the region between -3 and 1, including -3.
04

- Write (b) in interval notation

Using the graph, write the interval notation for the solution set:Therefore, the interval notation is \([-3, 1)\).
05

- Graph the inequality for (c)

To graph \(0 \leq x \leq 1.5\) on a number line:1. Draw a number line with numbers including 0 and 1.5.2. Use a closed circle at 0 to show that 0 is included in the solution.3. Draw another closed circle at 1.5 to show that 1.5 is also included.4. Shade the region between 0 and 1.5, including both endpoints.
06

- Write (c) in interval notation

Using the graph, write the interval notation for the solution set:Therefore, the interval notation is \[0, 1.5\].

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.

Number Line
A number line is a visual representation of numbers on a straight line. It helps you see the order and spacing of numbers.
For example, when graphing inequalities, a number line helps you identify which numbers are included in a particular range.

Let's look at how to graph inequalities using the number line:
  • First, draw a horizontal line and mark off key numbers (like -5, 0, 1, etc.).
  • Next, use open or closed circles to denote whether endpoints are included or excluded in the inequality.
  • Finally, shade the region that represents all the solutions to the inequality.
For instance, to graph \(-5 < x < 2\), plot open circles at -5 and 2, then shade the region between these two points.
Interval Notation
Interval notation is a way to describe a range of numbers, often used to express solutions to inequalities.
It uses brackets and parentheses to show which endpoints are included or excluded.

Here is a quick guide to interval notation:
  • Use (a, b) if both endpoints are excluded (open circles).
  • Use [a, b] if both endpoints are included (closed circles).
  • Combine brackets and parentheses for mixed cases like [a, b) or (a, b].
For example, \(-3 \leq x < 1\) in interval notation is written as \([-3, 1)\), meaning -3 is included and 1 is not.
Inequalities
Inequalities show the relationship between two values, indicating whether one is less than, greater than, or possibly equal to the other.

Common symbols used in inequalities:
  • \(<\) means less than.
  • \(\leq\) means less than or equal to.
  • \(>\) means greater than.
  • \(\geq\) means greater than or equal to.
When graphing inequalities, remember to use:
  • Open circles for \(<\) and \(>\).
  • Closed circles for \(\leq\) and \(\geq\).
For example, \(0 \leq x \leq 1.5\) means all numbers between 0 and 1.5, including both endpoints. This is represented by a shaded region between 0 and 1.5 with closed circles at both ends.

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

In your own words, explain how to solve the absolute value inequality, \(|3 x-2| \geq 4\).

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$ x<2 \text { or } x \geq 5 $$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$ x \leq-4 \text { or } x>-3 $$

Solve. $$ |6-x|=|3-2 x| $$

In \(2004,\) a water taxi sank in Baltimore harbor and five people drowned. The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied 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.