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Chapter 1: Problem 56

Find each absolute value. \(-|19|\)

Short Answer

Expert verified
-19

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from zero on a number line, regardless of direction. It is always a non-negative number. The absolute value of 19 is written as \(|19|\) and equals 19.
02

Evaluate the Absolute Value

Thus, \(|19| = 19\).
03

Apply the Negative Sign

Now, apply the negative sign outside the absolute value. This means we need to find \(-|19|\). Since \(|19| = 19\), we have \(-|19| = -19\).

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Key Concepts

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

Absolute Value Definition
Absolute value is a fundamental concept in mathematics. It measures the distance of a number from zero on the number line, without considering the direction. In simpler terms, it tells us how far a number is from zero, whether it's to the left or right. Absolute values are always non-negative, which means they are either positive numbers or zero.
For example:
  • \rThe absolute value of 5 is written as \( |5| \) and equals 5.
  • \rThe absolute value of -5 is written as \( |-5| \) and also equals 5.

Notice that both positive and negative versions of the same number have the same absolute value. This is because absolute value only considers distance, not direction.
Evaluating Absolute Values
Evaluating absolute values is very straightforward. To evaluate, you simply take the number inside the \( | | \) symbols and determine its distance from zero.
Here's how you can do it:
  • \rIdentify the number inside the absolute value bars.
  • \rIgnore the sign (positive or negative) of the number.
  • \rWrite the number as a positive value.

For example, let's evaluate the absolute value of 19:
\r
  • Step 1: Identify the number: 19
  • \rStep 2: Ignore the sign (it's already positive): 19
  • \rStep 3: Write the result: |19| = 19

In this case, \( |19| \) is simply 19. Remember, the same process applies if the number were negative. If we were to evaluate \( |-19| \), the result would also be 19, because we only care about the distance from zero.
Negative Sign Application
Now that we understand absolute values, let's learn how to apply a negative sign to them. When there is a negative sign outside the absolute value symbols, it affects the final result by making it negative.
For instance, consider \( -|19| \):
  • Step 1: Evaluate the absolute value inside the symbols: \( |19| = 19 \).
  • \rStep 2: Apply the negative sign to the result: -19.

This means \( -|19| = -19 \).
Whenever there is a negative sign outside the absolute value bars, follow these steps:
  • \rFirst, calculate the absolute value of the number inside.
  • Second, apply the negative sign to the resulting positive value.

By doing this, you're effectively changing the distance measurement into a negative number. This is useful in many mathematical contexts.

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Most popular questions from this chapter

Use the distributive property to rewrite each expression. $$ -\frac{1}{5}(5 x-7) $$

Use the distributive property to rewrite each expression. $$ -5.2(4 x+2.3) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\frac{5 y^{2}+4}{x}\)

Solve each problem. In August, Susan began with a checking account balance of \(\$ 904.89 .\) She made the following withdrawals and deposits.$$ \begin{array}{|c|c|} \hline \text { Withdrawals } & \text { Deposits } \\ \hline \$ 35.84 & \$ 85.00 \\ \$ 26.14 & \$ 120.76 \\ \$ 3.12 & \\ \hline \end{array} $$ Assuming no other transactions, what was her new account balance?

Use the distributive property to rewrite each expression. $$ -\frac{1}{3}(9 x-4) $$
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