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Chapter 1: Problem 58

Evaluate each absolute value expression. $$|-13|$$

Short Answer

Expert verified
| -13 | is 13.

Step by step solution

01

Understanding Absolute Value

In this step, we need to understand what an absolute value is. The absolute value of a number is its distance from zero on a number line, regardless of direction. It is always non-negative.
02

Apply Absolute Value Definition

To find the absolute value of -13, we need to evaluate how far -13 is from 0. Since absolute value ignores the negative sign, \(-13\) is at the same distance as 13 from 0 on the number line.
03

Calculate the Result

The distance of -13 from 0 on the number line is 13. Hence, the absolute value of -13 is 13. Therefore, \(|-13| = 13\).

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Key Concepts

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

Number Line
A number line is a visual tool that helps us understand numbers and their relationships. Imagine a horizontal line where numbers are placed in increasing order from left to right.
  • Zero is located at the center.
  • Positive numbers are on the right of zero.
  • Negative numbers are on the left of zero.
A number line is useful for visualizing how close or far numbers are from one another. When dealing with absolute values, the number line helps show how a number is positioned relative to zero. By observing this, you can easily determine the absolute value of any given number.
Non-Negative
The term "non-negative" refers to numbers that are either positive or exactly zero. Non-negative numbers do not include any negative numbers.
In mathematics, when we discuss absolute values, the result is always non-negative. This is because absolute value measures the magnitude of a number without considering direction.
For example, the absolute value of both -8 and 8 is 8. Both
  • 8 is already positive, and
  • -8 becomes 8 when processed through absolute value, removing the negative sign.
Thus, non-negativity ensures that absolute values provide a consistent measure of distance on the number line without any negative values.
Distance from Zero
The absolute value of a number reflects its distance from zero on the number line.
This measurement disregards whether the number is positive or negative and focuses solely on how far away that number is from zero.
  • For positive numbers, the distance is simply the number itself.
  • For negative numbers, the distance is the same as if they were positive, thus eliminating the negative sign.
For example, the distance from zero for -13 is 13, which is why the absolute value of -13 is 13. The concept is straightforward: just measure how far the number is from zero, ignoring its direction, to understand its absolute value.

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Most popular questions from this chapter

Solve the pair of simultaneous equations using any method 鈥揺limination, substitution or the graphical features of your GDC. $$\begin{aligned} &3.62 x-5.88 y=-10.11\\\ &0.08 x-0.02 y=0.92 \end{aligned}$$

Perform the indicated operation and simplify. $$\frac{3 x^{2}-3}{6 x} \times \frac{5 x^{2}}{1-x}$$

Determine whether each statement is true for all real numbers \(x\). If the statement is false, then indicate one counterexample, i.e. a value of \(x\) for which the statement is false. $$x^{3}+x>x^{3}$$

Use the substitution method to solve each pair of simultaneous equations. $$\begin{aligned} &2 x-y=-2\\\ &4 x+y=5 \end{aligned}$$

Find all values of \(x\) that make the equation true. $$\left|\frac{6-2 x}{3}\right|+\frac{2}{5}=8$$
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