The Absolute Value Equation: Understanding |x| and Solving Absolute Value Equations

Equation for Absolute Value

The equation for absolute value, often represented as |x|, is a mathematical expression that computes the magnitude or distance of a given number from zero on the number line

The equation for absolute value, often represented as |x|, is a mathematical expression that computes the magnitude or distance of a given number from zero on the number line. It always results in a non-negative value or zero.

The absolute value function can be defined as follows:

For a real number x, the absolute value of x, denoted as |x|, is defined as:

|x| = x, if x ≥ 0
|x| = -x, if x < 0 In simpler terms, if x is a positive number or zero, the absolute value of x is equal to x itself. If x is negative, the absolute value of x is equal to the negation of x. For example: - The absolute value of 5 (|5|) is 5. - The absolute value of -3 (|-3|) is 3. - The absolute value of 0 (|0|) is 0. The absolute value equation can also be used in solving absolute value equations, which involve finding the values of x for which the equation holds true. These equations often have two cases to consider due to the possibility of |x| being positive or negative. In such cases, we need to isolate the absolute value expression and set up two equations, one for when x is positive (x = |expression|) and one for when x is negative (x = -|expression|). These two equations can then be solved separately to find the possible solutions for x.

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