/*! 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 13 Write each inequality in interva... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 13

Write each inequality in interval notation, and graph the interval. \(t>4\)

Short Answer

Expert verified
(4, \, \infty)

Step by step solution

01

Understand the Inequality

The given inequality is \( t > 4 \). This means that \( t \) includes all numbers greater than 4 but does not include 4 itself.
02

Write the Inequality in Interval Notation

To write \( t > 4 \) in interval notation, note that we start from 4 (but do not include it), and go to infinity. Thus, the interval notation is \( (4, \, \infty) \).
03

Graph the Interval

To graph the interval \( (4, \, \infty) \), draw a number line. Place an open circle at 4 to indicate that 4 is not included. Then, shade the line to the right of 4 to show that all numbers greater than 4 are included.

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.

inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. In this exercise, we have the inequality: \(t > 4\). This inequality means that the variable \(t\), which represents a number, can be any value greater than 4 but cannot be equal to 4.
Inequalities can come in various forms, such as:
  • \(a > b\) - \(a\) is greater than \(b\)
  • \(a < b\) - \(a\) is less than \(b\)
  • \(a \geq b\) - \(a\) is greater than or equal to \(b\)
  • \(a \leq b\) - \(a\) is less than or equal to \(b\)

Understanding inequalities is crucial for solving and graphing them effectively. In the given example, \(t > 4\), we are only considering values greater than 4.
number line
A number line is a visual representation of numbers plotted on a straight line. It helps us understand the position and order of numbers.
To effectively use a number line for graphing inequalities, follow these steps:
  • Draw a horizontal line and mark evenly spaced points for numbers.
  • Identify the critical point (in our case, the number 4) on this line.
  • If the inequality sign is 'greater than' (\(>\)) or 'less than' (\(<\)), use an open circle to indicate that the value at that critical point is not included.
  • If the inequality sign is 'greater than or equal to' (\(\geq\)) or 'less than or equal to' (\(\leq\)), use a closed circle to indicate that the value at that critical point is included.

For our inequality \(t > 4\), we place an open circle at 4 because 4 itself is not included in the solution.
graphing intervals
Graphing intervals helps visualize the set of numbers that satisfy an inequality. The steps to graph the interval \((4, \, \infty)\) are:
  • Draw a number line.
  • Place an open circle at the number 4.
  • Shade the area to the right of the number 4.

The open circle at 4 shows that 4 is not part of the solution. The shaded line to the right indicates that all numbers greater than 4 are included, extending to infinity.
This method allows us to see all potential solutions to the inequality instantly, making it an invaluable tool for understanding and presenting inequalities visually.

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 each formula for the specified variable. \(P=4 s\) for \(s\)

Write the answer to each problem in terms of the variable. Cliff has \(r\) quarters. Express the value of the quarters in cents.

Brains Busters Solve each problem. Kevin is three times as old as Bob. Three years ago the sum of their ages was 22 yr. How old is each now? (Hint: Write an expression first for the age of each now and then for the age of each three years ago.)

A laptop computer with a regular price of \(\$ 597\) is on sale at \(20 \%\) off. Find the amount of the discount and the sale price of the computer.

Translate each statement into an inequality. Use \(x\) as the variable. You must be at least 18 yr old to vote.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.