On writing piecewise function with absolute value removed |Why is X & # 178; - 4x | written as X & # 178; - 4x (x ≤ 0) - X & # 178; + 4x (0 < x < 4), X & # 178; - 4x (x ≥ 4) I know this is the form of piecewise function. I just don't know how to get rid of the absolute value to write this form. Don't tell me the answer directly according to the image. I want to know the effective method and idea to solve this problem

On writing piecewise function with absolute value removed |Why is X & # 178; - 4x | written as X & # 178; - 4x (x ≤ 0) - X & # 178; + 4x (0 < x < 4), X & # 178; - 4x (x ≥ 4) I know this is the form of piecewise function. I just don't know how to get rid of the absolute value to write this form. Don't tell me the answer directly according to the image. I want to know the effective method and idea to solve this problem

For | a |, when a ≥ 0, | a | = a
When a