/*! 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 3 Evaluate each expression. $$|-... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 3

Evaluate each expression. $$|-6|$$

Short Answer

Expert verified
The absolute value of $$-6$$ is $$6$$ .

Step by step solution

01

Understanding Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering direction. This means it is always non-negative.
02

Compute the Absolute Value

To find the absolute value of $$-6$$ , we look at how far $$-6$$ is from zero. Since $$-6$$ is 6 units away from zero on the number line, $$|-6| = 6$$ .

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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 representation of numbers along a straight line. This tool helps visualize how numbers relate to each other and to zero. On a number line, numbers increase as you move to the right and decrease to the left. Zero is the central point.
  • Positive numbers are to the right of zero.
  • Negative numbers are to the left of zero.
  • Each point on the line represents a unique number.
Using the number line helps in understanding the concept of absolute value because it shows exactly how far a number is from zero. For example, if you look at data{\(-6\)}, it is located to the left of zero, 6 units away. Visualization on the number line helps confirm that the absolute value of \(-6\) is 6.
Distance from Zero
The distance from zero determines the absolute value of a number. Absolute value focuses solely on how far a number is from zero, disregarding whether the number is negative or positive.
To calculate this distance, simply count the units between your number and zero on the number line. This measures the magnitude of the number, which is always considered a positive distance.
For instance:
  • Number \(-6\): 6 units away from zero, so absolute value is 6.
  • Similarly, \(+6\) is also 6 units away, making its absolute value 6.
This process highlights that absolute value is all about distance, not direction.
Non-Negative Value
A non-negative value is any number that is either positive or zero. Absolute values are always non-negative because they represent the magnitude or size of a number in terms of distance from zero.
No matter how negative a number is, its absolute value is expressed as a non-negative number. This is because absolute value ignores whether the number is positive or negative, focusing only on its size.
In calculations:
  • Absolute value of \(-6\) is 6, a non-negative number.
  • Similarly, absolute value of \(0\) is 0, which is not negative.
  • Absolute value of any positive number remains unchanged.
This principle is crucial, especially in mathematical contexts where distances or magnitudes are discussed without the need for direction.

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Most popular questions from this chapter

Use a graphing utility to graph the equations and to approximate the \(x\) -intercepts. In approximating the \(x\) -intercepts, use a "solve" key or a sufficiently magnified view to ensure that the values you give are correct in the first three decimal places. Remark: None of the \(x\) -intercepts for these four equations can be obtained using factoring techniques.) $$y=x^{5}-6 x^{4}+3$$

The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show the interval(s) on a number line. $$|x-1| \leq \frac{1}{2}$$

Determine the center and the radius for the circle. Also, find the \(y\) -coordinates of the points (if any) where the circle intersects the \(y\) -axis. $$4 x^{2}-4 x+4 y^{2}-63=0$$

(a) Use a graphing utility to graph the following three parallel lines in the standard viewing rectangle: \(y+4=-0.5(x-2) ; y-3=-0.5(x+2) ; y=-0.5 x\) (b) Experiment with different settings for \(\mathrm{Xmin}, \mathrm{Xmax}\) Ymin, and Ymax. In each case, do the three lines still appear to be parallel?

Find the \(x\) - and \(y\) -intercepts of the line, and find the area and the perimeter of the triangle formed by the line and the axes. (a) \(3 x+5 y=15\) (b) \(3 x-5 y=15\)
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