Absolute Value Equations

Absolute Value Equations A mathematical statement, which shows that the absolute value of an expression is equal to the other expression, is called an absolute value equation. For example: - If the expressions | 3 x 5 | and x + 8 are equal, we write: | 3 x 5 | = x + 8; which is an absolute value equations. Similarly other examples are: - If the expression | x 30 | is equal to 10, it is written as: | x 30 | = 10 Absolute value of 7 subtracted from a number ( x ), equals 4, | x 7 | = 4 An absolute value of a certain number ( x ) is multiplied by 4, equals 20, | 4 x | = 20 Absolute of x divided by 7, equals 2, | x / 7 | = 2 Question 1: - Find x when | x 30 | = 10 Solution: - | x 30 | = 10 Case 1: - +(x 30) = 10 x 30 = 10 x = 10 + 30 x = 40 Case 2: - - (x 30) = 10 - x + 30 = 10 - x = 10 30 - = -20 x = 20 Question 2: - Find the value of x when | 4 x | = 20 Solution: - | 4 x | = 20 Case 1:- |4x| = 20 +4x = 20 x = 5 Case 2: - -4x=20 x = -5