Problem 62 - Beginning and Intermediate Algebra

Question

Find each absolute value. \(-|9-4|\)

Step-by-Step Solution

Answer

-5

Step 1: Calculate the expression inside the absolute value

First, compute the expression inside the absolute value -|9-4|. Calculate 9 i − 4 = 5.

Step 2: Apply the absolute value

Next, take the absolute value of the result from Step 1. The absolute value of 5 is simply 5. |-| 5|. = 5.

Step 3: Apply the negative sign

Since the original expression has a negative sign outside the absolute value, apply it: -|-5| = -5.

Key Concepts

Absolute Value Calculation

In mathematics, the absolute value of a number refers to its distance from zero on the number line, regardless of direction. To find the absolute value of a number, you simply ignore any negative sign. For instance, the absolute value of both 5 and -5 is 5, because both are five units away from zero.

Steps:
- Identify the number you want the absolute value for.
- Remove the negative sign if there is one.

Example: For the expression ewline |9-4|, calculate the subtraction first: 9 - 4 = 5.

Then, take the absolute value: |5| = 5.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division using whole numbers. When performing integer operations, it's important to remember the rules for positive and negative numbers.

For addition and subtraction:

• Add positive integers as usual.
• To subtract, add the opposite (e.g., subtract 4 is the same as adding -4).

Example: If we have the integers 9 and 4, for subtraction you do 9 - 4 = 5. If you needed to add them, 9 + 4 would be 13. Operations within parentheses or absolute value symbols always come first.

Order of Operations

Order of operations is a fundamental concept in mathematics. It dictates in which order you should perform operations to get the correct result. The standard order is:

1. Parentheses (inside them first)
2. Exponents (powers and roots)
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Let's apply the order of operations to the given exercise ewline -|9-4|.
First, solve inside the absolute value: 9 - 4 = 5.
Then, find the absolute value: |5| = 5.
Finally, apply the external negative sign to get the result: -5.