How do you solve equations involving absolute value? - Answers

Definition of Absolute Value: Absolute Value is the constant distance from zero; meaning that the distance from zero for any number, both positive and negative, is the same for each individual number.Example: Find the absolute value of " l -123 l "The distance from -123 from zero and the distance from 123 is the same; this goes for any number.Absolute value of l -123 l is equal to 123.*Note* Absolute Value is always Positive.Now, onto the infamous equations involving absolute value.Let's make up an equation.l 2x + 2 l = 26To find the value of X, you must always assume the existence of both positive and negative solutions; hence, it is called absolute value as explained above.Set up two equations; one for positive, one for negative.2x + 2 = 26 2x + 2 = -26Solve individually for X.2x + 2 = 26Subtract 2 from each side.2x = 26 - 22x = 24Divide 2 on each side.x = 12Onto the other equation.2x + 2 = -26Similarly, subtract 2.2x = -28Divide by 2.x = -14The two solutions are x = 12 and x = -14 which can be denoted by:X {12, -14}*To Check for Extranneous Solutions; ALWAYS substitute the values back in to see if they are valid.*