Problem 14 - Elementary Algebra

Question

Determine each of the values, |-10|

Step-by-Step Solution

Answer

Answer: The absolute value of -10 is 10.

Step 1: Identify the number

Identify the given number for which we will find the absolute value. In this case, the given number is -10.

Step 2: Apply the absolute value formula

The absolute value of a number is denoted as |x|, where x is any number. |x| = x if x is positive or zero and |x| = -x if x is negative. So, we can evaluate the | -10 |.

Step 3: Apply the rule to the given number

According to the formula, since -10 is a negative number, we have | -10 | = -(-10).

Step 4: Perform the calculation

When we negate the negative number -10, we get |-10| = 10. So, the absolute value of |-10| is 10.

Key Concepts

Understanding Negative Numbers

Negative numbers are a type of number that is less than zero. They are usually denoted with a minus sign (-) before the number, like -10 in our exercise.
Negative numbers are very common in everyday life. For example, temperatures below freezing are often described with negative numbers.
Here are some quick facts about negative numbers:

• They are located to the left of zero on the number line.
• Adding a negative number is the same as subtracting the corresponding positive number.
• Multiplying two negative numbers results in a positive number.

Understanding negative numbers helps in correctly finding absolute values, as seen in the exercise where |-10| becomes 10.

The Role of a Number Line

A number line is a visual representation of numbers in a straight line.
It's useful for understanding the position and relation between different numbers, including positive and negative numbers.
Here's what a number line typically shows:

• Zero is placed at the center.
• Positive numbers are placed to the right of zero.
• Negative numbers are placed to the left of zero.

The number line aids us in visualizing the concept of absolute value. For |-10|, you can see that moving from -10 to 10 on the number line simply comes down to finding its distance from zero, which is always positive.

Exploring Mathematical Formulas

Mathematical formulas are equations that provide a rule or relationship between different quantities.
The formula for absolute value, |x|, is handy when working with both positive and negative numbers.
The absolute value formula provides a simple rule:

• If the number is positive or zero, the absolute value is the number itself: |x| = x.
• If the number is negative, the absolute value is the opposite of the number: |x| = -x.

In the context of our problem, since -10 is negative, applying |x| = -x turns |-10| into 10. Formulas like these simplify solving such algebraic problems effectively.

Getting the Basics of Algebra Right

Algebra is a branch of mathematics that involves finding unknowns through equations and formulas.
Algebra basics include operations such as addition, subtraction, multiplication, and division, involving numbers and variables.
Here’s what to remember about algebra basics:

• Understand the components, which often include constants, variables, and operators.
• Learn how to manipulate expressions and equations, considering the rules like the absolute value rule.
• Apply basic operations properly to simplify expressions and solve for unknowns.

In our original exercise on absolute value, algebraic understanding helps in accurately performing negations or calculations, particularly with negative numbers, leading to correct solutions like finding that the absolute value of |-10| is 10.