Verified answer

Your use of parentheses is extensive without being in any way useful for avoiding ambiguity,

so I'll guess at one likely interpretation and solve that.

Also, please note that some displays of your main question were unreadable because Answers hides the back end of any string without spaces it decides is too long. Use some spaces to prevent it from doing that.

The interpretation I'm making of your inequality is this one:

(9/8) - (1/4)x + (7/8) ≥ 6x - (5/4)

(9/8) + (7/8) - (1/4)x ≥ 6x - (5/4)

(16/8) - (1/4)x ≥ 6x - (5/4)

2 + (5/4) ≥ 6x + (1/4)x

13/4 ≥ (25/4)x

(13/4)/(25/4) ≥ x

(13/4) (4/25) ≥ x

13/25 ≥ x

x ≤ 13/25