Problem 21 - Elementary Algebra

Question

Determine each of the values, |-1|

Step-by-Step Solution

Answer

Answer: The absolute value of -1 is 1.

Step 1: Analyze the problem

Identify the type of problem and the appropriate mathematical technique to apply.

Step 2: Apply the technique and solve

Answer: The absolute value of -1 is 1..

Step 3: Verify the result

Check the answer by substitution or alternative methods to confirm correctness.

Key Concepts

Understanding Negative Numbers

Let's dive into the world of negative numbers. Negative numbers are numbers less than zero. They are commonly found on the left side of the number line. Examples include -1, -5, and -100.

Negative numbers often represent values like debt or temperatures below freezing. They are opposed to positive numbers, which are greater than zero and found on the right side of the number line.

When working with negative numbers, it's important to understand their relationship with positive numbers. For instance, -1 is one unit away from 0, just like +1.

Negative numbers play a crucial role in finding the absolute value since absolute value measures how far a number is from zero, without regard to its sign.

Exploring Distance From Zero

The absolute value measures the distance from zero. It doesn't care if the number is positive or negative. Absolute value is always non-negative.

For example:

• The distance from 0 to +1 is the same as the distance from 0 to -1. Both have an absolute value of 1.
• The absolute value of -100 is the same as +100, which is 100 because both are equally spaced from zero.

Evaluating absolute values is straightforward. Simply remove any negative signs to find how far a number is from zero. When solving, remember that absolute value is denoted by vertical bars, such as \(|-3| = 3\) and \(|7| = 7\).

Keep in mind, no matter the original sign, absolute values are expressed as non-negative results.

Evaluation of Expressions Involving Absolute Values

Now, let's talk about evaluating expressions that include absolute values. Evaluating these involves interpreting the expression with the notion of distance from zero.

Consider the expression \(|-1|\). The absolute value sign tells us to find how far -1 is from 0, which is simply 1.

Here are the steps to evaluate:

• Identify the number inside the absolute value bars. If it's negative, like -1, remove the negative sign.
• The result is the absolute value, which is noted without any negative sign.

For any expression within vertical bars, treat it as a distance measure from zero. This process helps solve complex mathematical problems by simplifying negative or positive values to their neutral form. Always remember: the result of the absolute value operation is a non-negative number.