Problem 47 Find each absolute value and sim... [FREE SOLUTION]

Chapter 0: Problem 47

Find each absolute value and simplify if needed. $$ -|5| $$

Short Answer

Expert verified

The answer is -5.

Step by step solution

Understand the Absolute Value

The absolute value of a number is its distance from 0 on the number line, regardless of direction. This means the absolute value is always non-negative. For example, $ |5| = 5 $ and $ |-5| = 5 $.

Calculate the Absolute Value

In this case, first find the absolute value of 5. Since 5 is already positive, $ |5| = 5 $.

Apply the Negative Sign

Next, we apply the negative sign in front of the absolute value. So, we get $ -|5| = -5 $.

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Key Concepts

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

absolute value

The absolute value of a number is a measure of how far that number is from zero on the number line. It does not take into account whether the number is positive or negative. For example, both $|5|$ and $|-5|$ equal 5 because they are both the same distance away from zero. This concept can be especially useful in various types of mathematics, such as algebra and calculus. When simplifying expressions, always remember that the absolute value will turn any negative number inside the bars into a positive number. So, $|-10| = 10$ and $|7| = 7$.

number line

A number line is a visual representation of numbers in a straight, horizontal format. It typically includes both positive and negative numbers, centered around a zero point. The numbers to the right of zero are positive, and the numbers to the left are negative. For instance, on the number line, the distance between $2$ and $-3$ is fixed and can be easily visualized. Understanding how to position and read values on a number line is crucial for grasping the concept of absolute value. When finding the absolute value, you are essentially looking for the distance of any number from zero on this line.

negative sign

The negative sign (\-) indicates that a number is less than zero. However, when it comes to absolute values, this sign needs special attention. When calculating the absolute value, one must first remove any negative sign inside the absolute value bars. After finding the absolute value, if there's a negative sign outside, it will then be applied to the result. For example, in solving $-|5|$, step by step you first find $|5| = 5$. Then apply the negative sign, giving the final answer as $-5$. Properly managing the negative sign is crucial to getting the correct result.

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91影视

Find each absolute value and simplify if needed. $$ -|5| $$

Short Answer

Step by step solution

Understand the Absolute Value

Calculate the Absolute Value

Apply the Negative Sign

Key Concepts

absolute value

number line

negative sign

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