/*! 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 55 Solve each equation or inequalit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 55

Solve each equation or inequality. $$|10-4 x| \geq-4$$

Short Answer

Expert verified
All real numbers.

Step by step solution

01

Understand the Inequality

The given inequality is \(|10-4x| \geq -4\). Recall that the absolute value of any expression is always non-negative. Therefore, the absolute value will always be greater than or equal to any negative number.
02

Solve the Absolute Value Inequality

Since the absolute value, \(|10-4x|\), is always non-negative and \(-4\) is negative, \(|10-4x| \geq -4\) is always true for all real numbers.
03

State the Solution

Thus, the inequality is satisfied for all real numbers \(x\).

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.

Absolute Value
Absolute value is a fundamental concept in mathematics. It measures the distance of a number from zero on the number line, regardless of direction. For any real number \(a\), the absolute value is denoted by \(|a|\). This means:
  • |a| is always a non-negative value.
  • |a| equals a if a is non-negative (i.e., a follows: \(a \ge 0\).
  • |a| equals \(-a\) if a is negative (i.e., a follows: \(a < 0\).
For example, \(|3| = 3\) and \(|-3| = 3\). Absolute value treats every number as its positive counterpart.
Inequalities
Inequalities are statements that compare two values or expressions, showing if one is greater, less, or equal under certain conditions. They play a crucial role in solving problems with ranges of possible solutions. Common inequality symbols are:
  • \(\textless\textbackslashtextgreater\) - less than/greater than
  • \(\textleq\textbackslashtextgeq\) - less than or equal to/greater than or equal to
Remember, when multiplying or dividing inequalities by a negative number, the inequality sign flips direction. Inequalities help in understanding ranges of solutions rather than single values.
Real Numbers
Real numbers include all rational and irrational numbers, covering any number along the infinite number line. This includes:
  • Whole numbers like 0, 1, 2
  • Fractions like 1/2
  • Decimals like 3.14
  • Irrational numbers like \(\pi\)
The set of real numbers is represented by \(\textbackslashmathbb\textbackslashR\). They form the foundation of most calculations encountered in algebra and everyday math.

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 equation or inequality. $$|5 x+2|-2<3$$

Solve each rational inequality. Write each solution set in interval notation.4 $$\frac{2 x-3}{x^{2}+1} \geq 0$4

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{-5}{i}$$

Solve each equation or inequality. $$\left|5 x+\frac{1}{2}\right|-2<5$$

Solve each equation or inequality. $$|4 x+3|>0$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.