/*! 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 8 Simplify the following problems.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 8

Simplify the following problems. $$ -|16| $$

Short Answer

Expert verified
Answer: The simplified expression for -|16| is -16.

Step by step solution

01

Find the absolute value of 16

First, find the absolute value of 16, which is the distance of 16 from 0 on the number line. The absolute value is represented by the symbol | |, so we have |16| = 16.
02

Multiply by the negative sign

Now, we have to multiply the result from Step 1 by the negative sign outside the absolute value. So, we get -|16| = -(16) = -16.
03

Final Answer

The simplified expression for -|16| is -16.

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.

Simplifying Expressions
When working with mathematical expressions, the goal often is to make them simpler or easier to understand. This is where simplifying expressions comes into play. It involves reducing an expression to its most basic form. For example, if an expression includes unnecessary symbols or terms, these can be combined or reduced.

In the case of absolute values, simplifying might start with finding the distance of a number from zero and then applying any other operations such as multiplication or addition afterwards. It's much like cleaning up writing by removing extra words that aren't needed. Remember, the simpler the expression, the easier it is to work with in later calculations.
  • Simplifying makes solving equations quicker.
  • It reduces chances for mistakes in future calculations.
  • It provides a clear understanding of the mathematical problem at hand.
Negative Sign
The negative sign in math tells us to take the opposite value of a number. When you see a minus sign (-), it often means to reverse the direction or significance of a number. When combined with absolute values, such as -|16|, it often causes confusion without a deeper understanding.

Here鈥檚 how the negative sign works with our example: First, calculate the absolute value of 16, which is 16. Then, apply the negative sign resulting in -16. The negative sign does not change the number itself, just its direction on the number line.
  • The negative sign flips the value's direction.
  • Pay attention to its position relative to other signs and numbers.
  • It turns positive numbers to negative and vice versa.
Number Line Distance
Understanding absolute value involves comprehending the concept of number line distance. Absolute value expressions like |16| represent how far a number is from zero on a number line, regardless of direction. It always results in a positive number or zero.

Imagine a number line:
  • Zero is in the center;
  • Positive numbers increase to the right;
  • Negative numbers extend to the left.
So, when we measure something like |16|, we鈥檙e essentially counting 16 units away from zero. It's important to realize that absolute value ignores direction, focusing solely on distance.
  • Absolute values are always positive or zero.
  • They help in finding how far apart numbers are without considering direction.
  • They're crucial in simplifying expressions involving distance.

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

Convert the numbers used in the following problems to scientific notation. In 1981 , a Japanese company built the largest oil tanker to date. The ship has a mass of about 510,000,000,000 grams. This oil tanker is more than 6 times as massive as the U.S. aircraft carrier, U.S.S. Nimitz.

Convert the numbers used in the following problems to scientific notation. An atom of the chemical element bromine has 35 electrons. The mass of a bromine atom is 0.000000000000000000000000031 gram.

For the following problems, convert the numbers from scientific notation to standard decimal form. A photon is a particle of light. A 100 -watt light bulb emits \(1 \times 10^{20}\) photons every second.

Convert the numbers used in the following problems to scientific notation. Amino acids are molecules that combine to make up protein molecules. The amino acid tryptophan has a mass of 0.000000000000000000000340 gram.

Find the value of each of the following expressions. $$ -4(1-8)+3(10-3) $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics 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.