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Chapter 3: Problem 41

Evaluate each of the following: $$-8-8$$

Short Answer

Expert verified
-16

Step by step solution

01

Understanding the Problem

The given problem asks for the evaluation of the expression oindent \[-8-8\]. This involves simple subtraction of integers.
02

Perform the Subtraction

Consider the expression oindent \[-8 - 8\]. Since both terms are negative, subtract 8 from -8, which results in:\((-8 - 8) = -16\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Numbers
When we talk about negative numbers, we are dealing with values less than zero. Negative numbers are often used to represent losses or deficiencies in various contexts.
Understanding negative numbers is crucial because real-world problems frequently involve them.
Here are some key points:
  • Negative numbers are written with a minus sign (-) in front of them.
  • They appear to the left of zero on a number line.
  • Negative numbers are less than any positive number.
In our problem, \(-8\), the number eight is negative because of the minus sign in front. Trying to visualize it, think of having a debt of eight dollars. If you owe eight more dollars, your debt increases, not decreases.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. These operations are the foundations of mathematics. Understanding how to perform these operations with both positive and negative numbers is crucial.
Here's a quick look at subtraction involving negative numbers:
  • When subtracting a positive number from a negative number, you move further left on the number line.
  • For example, \(-10 - 5 = -15\), indicating that if you subtract 5 from -10, you end up 15 units left of zero.
  • When subtracting a negative number from another negative number, you also move further to the left.
In our example, \(-8 - 8 = -16\), because we are essentially subtracting two negative quantities, which increases the negative value.
Basic Algebra
Algebra is a branch of mathematics that uses symbols to represent numbers and operations. Basic algebra involves solving equations and expressions like the one in this exercise.
Key points about basic algebra:
  • It helps us generalize arithmetic rules.
  • It deals with expressions that include variables, constants, and arithmetic operations.
  • Understanding the properties of numbers, like negative and positive, is fundamental.
In the given problem, we use basic algebraic principles to evaluate the expression. The operation here is subtraction involving negative numbers. By following the steps:
  1. Identify the terms: \(-8\ and -8\).
  2. Perform the operation: \(-8 - 8\).
  3. Result: \(-16\).
This simple application of algebra helps us solve more complex problems later.

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Most popular questions from this chapter

Perform the indicated operations and simplify as completely as possible. $$x^{2}\left(x^{3}-4 x\right)-\left(2 x^{5}-4 x^{3}\right)$$

Look at each of the following inequality statements and determine whether they make sense. Explain your answers. (a) \(-3x<3\) (e) \(3x>4\)

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. A jogger's heart rate \(N\) (in beats per minute) increases as his or her speed \(s\) (in feet per second) increases. A physiologist collects data on a particular jogger and finds that the equation \(N=1.67 s+55\) seems to fit the data quite well. According to this model, what speed would produce a heart rate of 85 beats per minute?

Perform the indicated operations on the given inequality. Sketch the resulting inequality on a number line. \(-x<3 ;\) multiply each side by \(-1\)

Evaluate the given expression. $$|5-9|-|-3-8|$$
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