Problem 72 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. \(|-6|\)

Step-by-Step Solution

Answer

The absolute value of |-6| is 6.

Step 1: Identify the Given Number

The given number is |-6|.

Step 2: Understanding Absolute Value

The absolute value of a number is its distance from zero. It disregards the negative sign, therefore, the result is always non-negative.

Step 3: Compute the Absolute Value

The absolute value of |-6| is 6, as its distance from zero is 6 units disregarding the direction.

Key Concepts

Evaluate Expressions

When evaluating mathematical expressions, it's important to understand what you are being asked to solve or simplify. For an expression like \(|-6|\), you need to use the rules that govern absolute values to find the solution.

To evaluate expressions that include absolute values:

• Identify the expression within the absolute value symbols, which in this case is \-6\.
• Apply the concept of absolute value, which means finding the distance of a number from zero on the number line.
• Disregard any negative sign since absolute value represents magnitude, not direction.

Following these steps for the expression \(|-6|\) gives us the evaluated result of 6.

Algebraic Concepts

Algebraic concepts help us solve various mathematical problems by utilizing different operations and properties. One such concept is the absolute value, an essential idea when working with algebraic expressions.

The absolute value of a number indicates its magnitude, which is always a non-negative number. In algebra, understanding this can simplify many processes:

• Absolute values ignore the sign of a number, making arithmetic operations simpler.
• They allow you to measure distance on the number line effectively since they only focus on size.
• This is useful in real-world situations where direction doesn't matter, only the amount of change or difference.

Knowing these concepts is crucial as they often appear in equations, inequalities, and word problems.

Non-Negative Numbers

Non-negative numbers are all numbers that are zero or greater. They include zero and all positive numbers. Absolute values make any number non-negative by giving its distance from zero as a positive quantity.

In mathematics, non-negative numbers are important for several reasons:

• The absolute value results are always non-negative, as they measure distance, not direction.
• Non-negative numbers ensure clarity in scenarios, like distances or weights, where negative values do not make practical sense.
• They simplify many mathematical operations since negative factors are unnecessary.

Understanding when a number is non-negative or how it is transformed into one is a basic skill that will benefit many areas in math and beyond.