Formula For Absolute Value
Before going to learn about the formula for absolute value, let us recall what is absolute value. The absolute value of any given number is its distance from 0. The distance is always a non-negative quantity. Thus, the absolute value is always non-negative. The absolute value of any number, x is represented by |x|. Let us see the formula for absolute value using the above example. Let's recap the points that help in representing the absolute values:
- The absolute value of x is represented by either |x| or abs(x).
- The absolute value of any number always results in a non-negative value.
- We pronounce |x| as 'mod x' or 'modulus of x.'
What is Formula For Absolute Value?
The formula for absolute value gives us the absolute value of any number which gives a result that is always positive. The formula for the absolute value can be well understood by the example. Let us see an example.
From the above example, |4| = 4. So we can say that |x| = x, for every x ≥ 0.
Also, we have |-4| = 4. It means, |-4| = -(-4) = 4. So we can say that:
|x| = -x, for every x < 0.
|x| = x, for every x >= 0.
Thus, the formula for absolute value is:
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Example 1: Find the absolute values of -1/3, 5, and -0.5, solve it by using the formula for absolute value.
Solution:
To find: The absolute values of -1/3, 5, and -0.5.
By the formula of absolute value, we know that the absolute value of any number is always non-negative.
Thus,
|-1/3| = 1/3
|5| = 5
|-0.5| = 0.5
Answer: |-1/3| = 1/3, |5| = 5, and |-0.5| = 0.5.
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Example 2: Solve the absolute value equation |x| = 7 by using the formula for absolute value.
Solution:
To solve: The given equation.
The given equation is, |x| = 7.
By the absolute value formula, |x| can be ± x depending on the sign of x. So we get
± x = 7
or,
x = ± 7
Answer: x = ± 7.
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