Understanding Absolute Value Equations | Solving, Cases, and Examples

absolute value equation

An absolute value equation is an equation in which the variable is enclosed within the absolute value symbol | |

An absolute value equation is an equation in which the variable is enclosed within the absolute value symbol | |. It represents the distance between a number and zero on the number line, regardless of whether the number is positive or negative.

The general form of an absolute value equation is |expression| = constant, where “expression” represents any algebraic expression and “constant” is a non-negative number.

To solve an absolute value equation, we need to consider two cases:

Case 1: |expression| = constant
In this case, the absolute value of the expression is equal to the constant. To find the solutions, we have to solve the equation twice, considering both the positive and negative values of the constant.

Case 2: |expression| < constant In this case, the absolute value of the expression is less than the constant. To find the solutions, we solve the given equation normally, considering the positive and negative values of the expression. Let's look at an example to understand the concept better: Example: Solve the absolute value equation |3x - 4| = 7. Case 1: 3x - 4 = 7 Solving this equation, we get: 3x = 7 + 4 3x = 11 x = 11/3 Case 2: -(3x - 4) = 7 Solving this equation, we have: 3x - 4 = -7 3x = -7 + 4 3x = -3 x = -1 So, the solutions to the given absolute value equation are x = 11/3 and x = -1.

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