Final answer:
The symbol '|x|' in mathematics represents the absolute value of x, which is the distance of x from zero on the number line and always non-negative.
Step-by-step explanation:
Understanding the Absolute Value Function
In mathematics, the symbol '|x|' represents the absolute value of x. The absolute value of a number is its distance from zero on the number line, without considering direction. It is always a non-negative number.
For example, the absolute value of both 5 and -5 is 5. This is because both 5 and -5 are five units away from zero on the number line.
In mathematics, '|x|' represents the absolute value of the variable 'x'.
The absolute value of a number is its distance from zero on the number line.
For example, if x = -3, then |x| = 3 because the distance from -3 to 0 is 3 units. If x = 5, then |x| = 5 because the distance from 5 to 0 is also 5 units.
When dealing with equations or inequalities, the absolute value can lead to two different scenarios: if an equation states |x| = a, where a is a positive number, there are two possible solutions for x: x = a or x = -a. However, if |x| is set equal to a negative number, the equation has no solution because absolute value cannot be negative.
Examples:
|-7| = 7
|0| = 0