answer this

-|8x+2| >-10        multiply throgh by -1 and change the direction of the inequality sign

 l8x + 2l  < 10      we have two equations here

Let's make this an equality and then we can figure out what the proper solution interval(s) might be

8x + 2 = 10                           and    8x + 2 = -10

subtract 2 from both sides

8x = 8                                     8x = -12 

divide both sides by 8

x = 1                                  x = - 12/8  →   x = - 3/2

Note that the proper solution interval will lie between these two values.....thus

-3/2 < x < 1

The graph here indicates that this solution is correct :

https://www.desmos.com/calculator/ah5tytaeku