/*! 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 1 Express each interval in set-bui... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 1

Express each interval in set-builder notation and graph the interval on a number line. $$(1,6]$$

Short Answer

Expert verified
The set-builder notation for the interval $(1,6]$ is \( x | 1 < x \leq 6 \). On a number line, this set is represented by a shaded or marked area between an open circle on 1 (excluding 1) and closed circle on 6 (including 6).

Step by step solution

01

Conversion to Set-builder Notation

To express the provided interval $(1,6]$ in set-builder notation, a format is used that describes the set containing all numbers on the real line that falls between 1 and 6, excluding 1 but including 6. The notation becomes \( x | 1 < x \leq 6 \). This reads as 'The set of all x such that x is greater than 1 and less than or equal to 6'.
02

Graphing on a Number Line

To graph this interval on a number line, one begins by drawing a straight line, labeling it with numbers from 1 to 6. Since 1 is excluded from the set, an open circle is placed just above number 1 on the line to recognize this. Because 6 is included in the set, a closed or filled circle is placed just above number 6. The area between the open circle on 1 and the closed circle on 6 is shaded or marked off to show all the values within this range.

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!

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

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).

A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is bent into a square. Find the length of each piece if the sum of the areas of these squares is to be 2 square inches.

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y_{1}=\frac{3}{x-1}, y_{2}=\frac{8}{x}, \text { and } y_{1}+y_{2}=3 $$

Write an original word problem that can be solved using a linear equation. Then solve the problem.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

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.