Problem 38 - Elementary Algebra

Question

\(|-36|\)

Step-by-Step Solution

Answer

|-36| = 36

Step 1: Understand Absolute Value

The absolute value of a number is the distance of that number from zero on a number line, regardless of direction. It is always non-negative.

Step 2: Apply Absolute Value Definition

Since absolute value measures distance from zero, \(|-36|\) means how far \(-36\) is from zero.

Step 3: Calculate the Distance

To find the absolute value, simply take the distance of \(-36\) from zero, which is \36\.

Key Concepts

Understanding Distance from Zero

When learning about absolute values, it's important to grasp the concept of 'distance from zero'.
Distance from zero means how far a number is from the number 0 on a number line.
For example, dash;36dash is 36 units away from zero.
This distance is always positive because distance cannot be negative.
So, when we calculate the absolute value of dash36, we are looking for how many steps it takes us to get back to zero, which is 36.

Explaining Non-Negative

Another key concept in understanding absolute values is that they are always non-negative.
Non-negative means a number that is either positive or zero, but it is never negative.
Numbers like 5, 0, and 8 are non-negative.
Even when you have a negative number, such as dash36, its absolute value will be a positive number.
This is because the concept of distance cannot be negative, which is why dash36 becomes 36 when we take its absolute value.

Visualizing on a Number Line

A number line is a visual representation that helps in understanding absolute values.
When you look at a number line, zero is typically placed in the middle.
Positive numbers extend to the right, and negative numbers extend to the left.
To find the absolute value of dash36, you would count 36 units to the right of zero.
This is why dash36 has an absolute value of 36, because it's 36 units away from zero on the number line.
Using this visual tool can make it much easier to grasp why the distance (or absolute value) of any number from zero is always non-negative.