Understanding Absolute Value in Mathematics | Definition, Examples, and Applications

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In mathematics, the expression |x| represents the absolute value of a number x

In mathematics, the expression |x| represents the absolute value of a number x. The absolute value of a number is its distance from zero on the number line, regardless of its sign.

To understand this concept, let’s consider a few examples:

1. If x is a positive number, such as x = 5, then |x| = 5. This is because 5 is 5 units away from zero on the number line, and the absolute value ignores the positive sign.

2. If x is a negative number, such as x = -3, then |x| = 3. This is because -3 is 3 units away from zero on the number line, and the absolute value considers only the distance, not the negative sign.

3. If x is zero, then |x| = 0. This is because zero is exactly at zero on the number line, so its absolute value is zero.

In summary, the absolute value function removes the negative sign of a number and gives the positive distance from zero. Mathematically, we can define the absolute value function as follows:

If x ≥ 0, then |x| = x.
If x < 0, then |x| = -x. The absolute value function is commonly used in various mathematical operations, equations, and inequalities. It also has applications in real-life scenarios, such as finding the magnitude of a vector in physics or calculating the difference between two values.

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