Solve for x in the same way you would a normal equality ***. Construct your interval based on the end inequality. Example: If x <= c, than the domain is (-infinity .. c]
Note: your book is wrong.
The problem looks to be: solve -3(x-4) <= 5 + x, in which case the book is correct.
x -3(x-4) <= 5 + x
-3x + 12 <= 5
-3x <= -7
x >= 7/3 NOT 7/4
Construct your interval accordingly.
Remember to flip your inequality when dividing by a negative number: Put this where *** is.
if a > b
then a - b > 0
then -b > -a
than -a < -b