Question 23201
I can't quite envision all the notation that is giving you trouble, and I haven't yet been able to get the section from my One Step online yet because of the graphing.  I can send you a Word file containing this section that might be easier to understand.  For now, at least, here is your current problem:

8x+ 8 > 7x + 9


Subtract 7x from each side:
8x-7x + 8 > 7x - 7x + 9
x+ 8 > 9


Now subtract 8 from each side:
x+8-8 > 9-8
x>1


This means that the solution set consists of all values of x (on a numberline) that are to the right of 1.  This would be like 2, 3, 4, 5, etc. including all fractional and decimal values as wll.  It goes right up to the 1, but it does NOT include the 1.  There are different notations for this.  Sometimes they put an open circle on the 1 and shade everything to the right of this open circle. 


If the answer had been {{{x>=1}}}, then this means everything to the right of 1 but in this case it also INCLUDES the 1.  We represent this with a SOLID circle, and shade everything to the right.


Another notation for NOT including the endpoint, instead of the open circle, is to use a parenthesis on the 1, where the parenthesis curves in the direction of the shaded region on the numberline.  


The corresponding notation that means to INCLUDE the endpoint would be to use a BRACKET [  instead of parenthesis opening in the direction of shading.


If the solution to the problem happens to be all values of x, then you have a numberline shaded with arrows on each end.  This means all real values of x.


If there is NO SOLUTION, then they probably used the greek letter for "phi", which is a 0 with a line through it like this: {{{phi}}}.  


Maybe that will help some.  Sorry I can't see your book.


R^2 at SCC