/*! 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 102 Write each inequality using inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 102

Write each inequality using interval notation. See Section 2.8. $$ x \leq 0 $$

Short Answer

Expert verified
The interval notation is \( (-\infty, 0] \).

Step by step solution

01

Understand the inequality

The given inequality is \( x \leq 0 \). It states that \( x \) can be any value less than or equal to 0.
02

Identify the range of values

Determine the range of values for \( x \) that satisfy the inequality \( x \leq 0 \). This includes all numbers from negative infinity to zero.
03

Write the interval notation

Convey this range in interval notation. For \( x \leq 0 \), this range can be expressed as \( (-\infty, 0] \). The parenthesis \( ) \) indicates that negative infinity is not a specific value but a bound, and the bracket \( ] \) means that 0 is included in the interval.

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
To understand inequalities, we must first grasp that they are mathematical expressions describing the relationship between two values. Inequalities use symbols to show if one value is greater than, less than, equal to, or not equal to another value.

If we encounter an inequality like \( x \leq 0 \), it tells us that \( x \) can be any value less than or equal to 0. Here, the symbol '鈮�' means 'less than or equal to'.

We can visualize these relationships on a number line:
  • For \( x < 0 \), we consider only the values strictly less than 0.
  • For \( x \leq 0\), we include 0 as well as all values below it.
In this way, inequalities are essential for defining ranges and sets of numbers that we can use further in algebra and calculus.
interval notation
Interval notation is a shorthand way to describe a range of numbers. It helps make sense of intervals by using parentheses and brackets.

In interval notation:
  • Parentheses ( ) are used to indicate that an endpoint is not included.
  • Brackets [ ] imply that an endpoint is included.
Let's put the inequality \( x \leq 0 \) into interval notation step-by-step:

1. The range of values for \( x \) includes all numbers from negative infinity to zero.
2. We write this interval as \( (-\infty, 0] \).
3. The parenthesis around -鈭� means that negative infinity is not a specific number but a bound.
4. The bracket around 0 shows that 0 is part of the interval.

This makes interval notation a clear and concise way to represent sets of numbers, which is particularly useful for understanding and solving inequalities.
range of values
The range of values in an inequality like \( x \leq 0 \) defines all possible numbers that satisfy it.

Steps to determine the range:
  • Identify the inequality and understand what values of \( x \) it represents.
  • For \( x \leq 0 \), we look for numbers that are less than or equal to 0. This includes all negative numbers and zero.
Visualize it on a number line: every value starting from -鈭� up to and including 0.

This range of values is then expressed in interval notation as \( (-\infty, 0] \). By knowing the range of values, we can better understand the solution set for an inequality. This approach can be applied to more complex inequalities as well, ensuring consistency and clarity in representing mathematical relationships.

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

An equation that defines \(y\) as a function \(f\) of \(x\) is given. (a) Solve for \(y\) in terms of \(x,\) and \(r e\) place \(y\) with the function notation \(f(x) .\) (b) Find \(f(3) .\) See Example 6 $$ -2 x+5 y=9 $$

Write each formula using the "language" of variation. For example, the formula for the circumference of a circle, \(C=2 \pi r,\) can be written as "The circumference of a circle varies directly as the length of its radius." \(\mathscr{A}=\frac{1}{2} b h,\) where \(\mathscr{A}\) is the area of a triangle with base \(b\) and height \(h\)

Solve each problem. The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the speed. If 242 Ib of force keeps a \(2000-\) -lb car from skidding on a curve of radius 500 ft at \(30 \mathrm{mph}\), what force would keep the same car from skidding on a curve of radius 750 ft at 50 mph?.

Graph each pair of equations on the same coordinate axes. $$ \begin{aligned} &2 x+3 y=12\\\ &4 x-2 y=8 \end{aligned} $$

Solve each problem. The current in a simple electrical circuit varies inversely as the resistance. If the current is 20 amps when the resistance is 5 ohms, find the current when the resistance is 7.5 ohms.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.