the shaded area defines where 'x' is valid and this can be manually examined by plugging in a couple of values for 'what if x=...'?  If x=1, then |4(1)-3|=|1|=1, etc. 

The shaded area is bounded by solid lines rather than dotted lines.  A dotted line would indicate that a value is not included (enter "|4x-3|<1" to check out the difference).