Question

How can you identify an extraneous solution of absolute value equations? Give an example

Answer 1

To identify an extraneous solution of absolute value equations, substitute the potential solutions back into the original equation and check if they satisfy the equation. If a solution does not satisfy the equation, it is considered extraneous.

Step-by-step explanation:

To identify an extraneous solution of absolute value equations, you need to substitute the potential solutions back into the original equation and check if they satisfy the equation. If a solution does not satisfy the equation, it is considered extraneous. For example, let's consider the equation |x - 3| = 5. By substituting x = 8 into the equation, we get |8 - 3| = 5, which is true. However, if we substitute x = 1 into the equation, we get |1 - 3| = 5, which is false. Therefore, x = 1 is an extraneous solution.

Answer 2

Absolute value of a number is the positive value of the number. ... To solve an absolute value problem, we first isolate the absolute value term and then separate the equation into two cases: the positive case and the negative case.