To clarify. I was able to solve it by writing all absolute values as positive numbers. But I am trying to understand why thats the correct answer. What is confusing me the most is finding intervals, identifying intervals and solving for each. I am getting this information from (apologize in advance if for some reason not allowed to post link)

Code:

https://www.symbolab.com/solver/linear-equation-calculator/-5%5Cleft%7C2%2B4x%5Cright%7C%3D-32%5Cleft(x%2B%5Cfrac%7B3%7D%7B4%7D%5Cright)-%5Cleft%7Cx%5Cright%7C%2B1

Looking at the steps, its showing 3 possible equations. Other, simpler absolute value equations I have done in the past indeed have to answers, a positive and negative, and need to solve for both. But those are in form of $\displaystyle |x|+3=5$, that gives me $\displaystyle x+3=5$ and $\displaystyle x+3=(-5)$ and solve for both.