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Chapter 1: Problem 43

Evaluate each expression. $$-|4|$$

Short Answer

Expert verified
-4

Step by step solution

01

Understand the Absolute Value

First, recognize that \(|4|\) represents the absolute value of 4, which is the distance of 4 from 0 on the number line, without considering direction. Therefore, \(|4| = 4\).
02

Apply the Negation

Now, we need to apply the negation outside the absolute value function. This means we take the result from Step 1 and place a negative sign in front of it: \(-|4| = -4\).

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Key Concepts

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

Algebraic Expressions
An algebraic expression consists of numbers, variables, and arithmetic operations. They are like sentences in math. When you solve an algebraic expression, you're performing operations to find a specific value. In our exercise, <em>-|4|</em> is a simple algebraic expression where you need to evaluate the absolute value and then apply the negation. Even though this specific expression doesn鈥檛 have variables, it follows rules that are common in algebra.
  • Begin with the innermost or most straightforward calculation.
  • Evaluate according to the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)鈥攐ften abbreviated as PEMDAS.
  • Combine like terms if applicable. In this case, we start by finding the absolute value, which is the expression inside the vertical bars.
Negation
Negation is a fundamental concept in mathematics that involves changing the sign of a number. If you negate a positive number, it becomes negative, and vice versa.

In the given exercise: Evaluate -|4|, once you've found the absolute value of 4, the next step is to apply negation.

Let's break it down:
  • The absolute value of 4 is 4, which we found in Step 1.
  • Applying negation to 4 changes it to -4, as shown in Step 2.


Negation is simply about flipping the sign, and it鈥檚 helpful to remember that negation affects whatever number it鈥檚 placed in front of.
Number Line
A number line is a visual representation of numbers in a straight line. Each point on the line corresponds to a number. This helps you understand the notion of positive and negative values and is especially useful for grasping the concept of absolute value.

  • The number '0' is usually the center point on the number line.
  • Positive numbers are located to the right of 0, and negative numbers are located to the left of 0.
  • When we talk about the absolute value of a number, we are talking about its distance from 0, without considering the direction.

For instance, on a number line:
  • The number 4 is four units to the right of 0.
  • Therefore, the absolute value of 4 is 4.
  • When negation is applied, like with -|4|, you simply shift the positive outcome to its equivalent negative position, moving to the left side of the number line.

This visual method can significantly aid in understanding how absolute value and negation work together.

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Most popular questions from this chapter

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In Exercises \(51-60,\) fill in as many of the following ordering symbols as make the statement true. Choose from \(<, \leq,>, \geq,=, \neq\). 25 - 5____14 + 3.

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