Modulus function

Question

Given that a>0, solve |2x+a|=|x|-a

Answer 1

given a>0, solve |2x+a|=|x|-a

there are four criteria combinations,,,x≥0 or x<0 and x≥-a/2 or x<-a/2

[(a or b} and (c or d)]

for ac,,,,, x=-2a is calculated solution, but that violates criteria x≥-a/2 meaning x=-2a not valid

for ad and bd,,, x=0 is calculated solution, but that violates criteria x<-a/2 meaning x=0 not valid

for bc,,,x=-2a/3 is calculated solution, but that violates x≥-a/2 criteria meaning x=-2a/3 not valid

there are no solutions.