/*! 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 75 Evaluate the following. See Sect... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 75

Evaluate the following. See Sections 1.2 and \(1.3 .\) $$ -(-6)-|-10| $$

Short Answer

Expert verified
The value is -4.

Step by step solution

01

Simplify the Double Negative

The first part of the expression is \(-(-6)\). According to the rules of integers, the negative of a negative number is positive. Therefore, \(-(-6) = 6\).
02

Evaluate the Absolute Value

The next part of the expression is the absolute value \(|-10|\). The absolute value of a number is always non-negative, and it reflects the distance from zero. Thus, \(|-10| = 10\).
03

Substitute and Calculate

Now substitute the simplified parts back into the expression. We have the expression as \(6 - 10\). Perform the subtraction: \(6 - 10 = -4\).

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 concept in mathematics that tells us the distance a number is from zero on the number line, without considering the direction. In simpler terms, it converts any number to a non-negative number no matter its original sign.
To calculate the absolute value, you simply ignore the sign of a number. Here鈥檚 how it works:
  • The absolute value of 10 is written as \(|10| = 10\).
  • The absolute value of -10 is written as \(|-10| = 10\). This is because -10 is 10 units away from zero on the number line.
Remember, the outcome of an absolute value operation is always positive or zero because it鈥檚 measuring distance, not direction.
Double Negative
The concept of double negative in math often confuses students, but it鈥檚 actually pretty straightforward. When you encounter two negative signs together, they effectively cancel each other out. This means a negative of a negative number results in a positive number.
For example, if you have \(-(-6)\), this becomes 6. You鈥檙e flipping the sign twice: once from negative to positive.
An easy way to remember:
  • Think of a double negative similar to grammar, where two negatives equal a positive.
  • Visually, seeing two dashes \(-(-)\) in math should remind you to flip the sign to positive.
This rule is handy and pops up frequently, especially in algebra and calculus.
Integer Subtraction
Integer subtraction can sometimes be tricky because it involves understanding how numbers work together on the number line. When you subtract integers, you take away a value, which might involve working with signs in ways that can be counterintuitive.
In basic terms, subtraction can be thought of as "adding the opposite". For example, when you see \(6 - 10\), you can interpret it as \(6 + (-10)\).
Here鈥檚 how it works:
  • Begin at 6 on the number line.
  • Move 10 units to the left (as you are adding negative ten).
  • You鈥檒l land on -4, which means \(6 - 10 = -4\).
Understanding and visualizing this method will help simplify integer subtraction, allowing you to be confident with negatives and positives.

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

The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count \(C\) for a serving of food can be computed using the formula \(C=4 h+9 f+4 p,\) where \(h\) is the number of grams of carbohydrate contained in the serving, \(f\) is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving. A serving of raisins contains 130 calories and 31 grams of carbohydrate. If raisins are a fat-free food, how much protein is provided by this serving of raisins?

Consider the equation \(3 x-4 y=12 .\) For each value of \(x\) or \(y\) given, find the corresponding value of the other variable that makes the statement true. If \(x=4,\) find \(y\)

Solar system distances are so great that units other than miles or kilometers are often used. For example, the astronomical unit \((A U)\) is the average distance between Earth and the sun, or \(92,900,000\) miles. Use this information to convert each planet's distance in miles from the sun to astronomical units. Round to three decimal places. The planet Mercury's AU from the sun has been completed for you. (Source: National Space Science Data Center). $$ \begin{array}{|l|c|c|} \hline \text { Planet } & {\text { Miles from the Sun }} & {\text { AU from the Sun }} \\ \hline \text { Mercury } & {36 \text { million }} & {0.388} \\ \hline \end{array} $$ Venus \(\quad 67.2\) million

Solve each inequality. Graph the solution set and write it in interval notation. $$ |0.6 x-3|>0.6 $$

Solve: \(2 x-3>5\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

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.