Question

Solve the absolute value equation and check for extraneous solutions:

|2x - 8| = -4x - 2

Answer 1

To solve the absolute value equation |2x - 8| = -4x - 2, we consider two cases and find that x = 0.0216 is the valid solution.

Step-by-step explanation:

To solve the absolute value equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2x - 8 = -4x - 2

Case 2: -(2x - 8) = -4x - 2

Solving for x in each case, we find x = -0.0224 or x = 0.0216.

However, we need to check if these solutions are extraneous. Plugging them back into the original equation, we find that x = 0.0216 is the valid solution.