Absolute Value: Definition, Applications, And Examples

Absolute Value

Absolute value makes a negative number positive. Positive numbers and 0 are left unchanged. The absolute value of x is written |x|.

Absolute value refers to the numerical value of a number without regard to its sign. It is denoted by enclosing the number between vertical bars or pipes. For example, the absolute value of -5 can be written as | -5 |, which is equal to 5.

In general, absolute value is used to find the distance between two points on a number line. For instance, the distance between 3 and -2 is | 3 – (-2) |, which equals 5. This is because we take the absolute value of the difference between the two numbers, which is 5.

In mathematics, absolute value has a number of important applications, particularly in solving equations and inequalities. For example, to solve the equation | x – 10 | = 3, we determine the two possible values of x that are 3 units away from 10, namely x = 7 and x = 13.

In addition, absolute value is useful in representing real-world quantities that cannot be negative, such as distance or time. For instance, if we know that a car is traveling at a speed of 60 miles per hour, we know that its speed can never be negative, so we take the absolute value of the velocity to obtain 60.

Overall, absolute value is an important concept in mathematics that has many practical applications in everyday life.

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