Absolute value represents a number's distance from zero on the number line, disregarding direction. It's crucial for calculating distances and magnitudes. This overview covers its properties, such as non-negativity and behavior in operations, and guides through solving equations and inequalities involving absolute values. Understanding these concepts is vital for mathematical applications and real-world scenarios requiring exact measurements.
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Absolute value represents the distance of a number from zero on the number line without considering direction
Denotation of Absolute Value
Absolute value is denoted by |x|, where x is any real number
Properties of Absolute Value
Absolute values are always non-negative, and the absolute value of a number and its opposite are equal
Understanding absolute value is essential in various applications, such as calculating distances and defining magnitudes
To solve an equation with an absolute value, one must isolate the absolute value, consider both positive and negative cases, and check solutions for validity
Solutions to absolute value equations can be represented on a number line, showing their respective distances from zero
Absolute value inequalities define a range of values based on their distance from zero and can be transformed into compound inequalities
By solving the compound inequality, one can determine the complete set of solutions that satisfy the original inequality
Solutions to absolute value inequalities can be depicted on a number line, showing the range of permissible values
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Absolute value notation
Denoted by |x|, where x is a real number.
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Absolute value of non-negative numbers
If x is non-negative, |x| equals x.
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Absolute value of negative numbers
If x is negative, |x| equals -x, making it non-negative.
