Question

Solve the absolute value equation 5K + 12/ |5K + 12| = 2/ | 4K-1 | where the lines indicate absolute value. Determine the values of KK that satisfy the given equation, considering both positive and negative solutions.

Answer 1

To solve the absolute value equation 5K + 12/ |5K + 12| = 2/ | 4K-1 |, we need to consider two cases based on the sign of the expression inside the absolute value.

Step-by-step explanation:

To solve the absolute value equation 5K + 12/ |5K + 12| = 2/ | 4K-1 |, we need to consider two cases based on the sign of the expression inside the absolute value.

Case 1: |5K + 12| is positive

When |5K + 12| is positive, the equation can be simplified to: 5K + 12/ (5K + 12) = 2/ |4K - 1|

Solving this equation gives us K = -1/2.

Case 2: |5K + 12| is negative

When |5K + 12| is negative, the equation can be simplified to: 5K + 12/ -(5K + 12) = 2/ |4K - 1|

Solving this equation gives us K = 5/4.

Therefore, the values of K that satisfy the equation are K = -1/2 and K = 5/4.