Problem 10 - Elementary Algebra

Question

Determine each of the values, |3|

Step-by-Step Solution

Answer

Answer: The absolute value of 3 is 3.

Step 1: Identify the expression inside the absolute value

We are given |3|, so the expression inside the absolute value is 3.

Step 2: Determine the absolute value

Since 3 is already a non-negative number, its absolute value is the same number. So, |3| = 3.

Key Concepts

Algebraic Expressions

When we talk about algebraic expressions in mathematics, we're referring to a combination of numbers, variables (like x or y), and arithmetic operations such as addition, subtraction, multiplication, and division. For example, in the expression \(7x + 3\), \(7x\) represents a multiplication of 7 with a variable \(x\), and \(+3\) is an addition operation applied to a constant number 3.

Understanding algebraic expressions is crucial for solving various algebra problems. An expression can be as simple as a single number or as complex as a series of operations with multiple variables. The beauty of algebraic expressions lies in their ability to represent real-world situations in a mathematical form, enabling us to solve problems by applying algebraic rules and simplifications.

Non-Negative Numbers

Non-negative numbers are simply numbers that are either greater than or equal to zero. They include all positive numbers along with the number zero itself. The main characteristic of non-negative numbers is that they do not include any negative numbers.

To better grasp this concept, picture the number line: it stretches infinitely in both directions. Non-negative numbers are found to the right of (and including) the zero point. These numbers are essential in various aspects of mathematics because they represent quantities that can't be less than nothing—such as the absolute values, distances, or amounts of objects.

Elementary Algebra

Elementary algebra, often the first grass-roots encounter of students with algebra, is the branch of mathematics that deals with the manipulation of algebraic expressions and solving algebraic equations. This foundational knowledge is essential as it introduces concepts like the use of variables to represent numbers and the rules for arithmetic operations applied to these variables.

In the context of the given exercise, where we are asked to determine the value of \(|3|\), elementary algebra teaches us the concept of the absolute value. The absolute value of a number is its distance from zero on the number line, regardless of direction. Since distance cannot be negative, the absolute value of any number is always a non-negative number. According to elementary algebra, the absolute value of any positive number or zero is the number itself, as it's already at or to the right of the zero point on the number line.