Problem 41 - Algebra 1

Question

Evaluate the expression. $$|7|$$

Step-by-Step Solution

Answer

7

Step 1: Understanding Absolute Value

An absolute value is the non-negative value of a real number without regard to its sign. It is denoted by either two vertical lines bracketing the number or expression.

Step 2: Evaluate the Absolute Value

For a positive number, its absolute value will simply be the number itself. Thus the absolute value of 7, which is already a positive number, is simply 7.

Key Concepts

Real Numbers

When we talk about real numbers, we refer to all the numbers that can be located on the number line. This includes positive numbers, negative numbers, zero, fractions, and decimals. Collectively, they form the set of real numbers, which is denoted by the symbol \( \mathbb{R} \). Real numbers encompass every possible value in continuous numerical space.

A few characteristics of real numbers include:

• They are infinite, meaning there's no end to how many real numbers exist on the number line.
• Real numbers can be whole numbers, fractions, or irrational numbers, like \( \pi \).

In understanding real numbers, it is crucial to grasp that every absolute value operation on a real number will result in a real number. This set doesn't include any imaginary or complex numbers, which are outside of our real number discussion.

Positive Numbers

Positive numbers are those that lie above zero on the number line. They are greater than zero and include whole numbers like 1, 2, 3, and so forth, as well as fractions and decimals such as 0.5 and 3.14.

Key aspects of positive numbers:

• They are used to represent quantities and measurements that have an increase or presence of something.
• Positive numbers are crucial for daily calculations, finances, and measurements.

When evaluating expressions that involve positive numbers, particularly in the context of absolute values, the result is direct and straightforward. The absolute value of a positive number is the number itself, making calculating the absolute value of a positive number a simple task.

Evaluate Expressions

Evaluating expressions involves finding the value of an algebraic expression by performing the operations indicated. This process can include adding, subtracting, multiplying, dividing, and applying operations like finding the absolute value.

Here are steps to efficiently evaluate expressions:

• First, identify any operations that need to be done first, such as expressions within parentheses or absolute value symbols.
• Proceed with the arithmetic operations in the conventional order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
• Finally, simplify the expression to find the answer.

For absolute values, like \( |7| \), the expression evaluates to 7 because the operation disregards any negative signs, making it a straightforward procedure, especially when dealing with numbers that are already positive. Understanding these fundamental steps makes evaluating any expression much easier and removes any confusion.