Explain the difference in meaning between |-3| and -3.
No explanation be sure to include mathematical various keys.
|-3| = 3 by the definition of absolute value
-3 is just the integer value of -3
The absolute value of a number, denoted by |x|, represents the distance of that number from zero on a number line. It is always a positive value or zero, regardless of the sign of the number. In contrast, a negative number, written as -x, simply represents the opposite of the positive value of x.
To better understand this difference, let's take the example of |-3| and -3:
|-3| represents the absolute value of -3. To find this value, we follow a simple rule: we ignore the sign of the number and consider only its magnitude. In this case, |-3| would be equal to 3 because the distance from -3 to 0 on the number line is 3 units. Hence, the absolute value of -3 is 3.
On the other hand, -3 is a negative number. It signifies that the number itself is negative. In this case, -3 means "the opposite of 3" or "negative 3".
So, in summary, |-3| is equal to 3, which represents the absolute value of -3 (ignoring its sign), whereas -3 is a negative number that signifies the value itself.