Andrax said:
The absolute value of a number is its distance from zero on the number line. It is always positive and is represented by two vertical bars surrounding the number, such as |3|.
To prove an absolute value equation, you must show that the equation holds true for both the positive and negative values of the variable. This can be done by substituting the positive and negative values into the equation and solving for each case.
Absolute value and modulus are often used interchangeably, but they have slightly different definitions. Absolute value is the distance from zero on the number line, while modulus is the numerical value of a number without its sign.
Yes, the properties of absolute value can be used to solve equations. These properties include the distance property, which states that the absolute value of a sum is equal to the sum of the absolute values, and the multiplication property, which states that the absolute value of a product is equal to the product of the absolute values.
Some common mistakes when solving absolute value equations include forgetting to consider both the positive and negative solutions, incorrectly applying the properties of absolute value, and not simplifying the equation correctly before solving for the variable.