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This problem trains for: SAT-I, AMC-8, GMAT.

How many integer values of x are there such that:

equation

Process the inequality algebraically:

equation

equation

equation

equation

and note that:

equation

equation

Build a table to summarize the sign of the algebraic fraction. The fraction is a division and obeys the rules of signs applicable to division:

x -∞....1....5.5....
2x-11−−−− −−−−−−−−−−−−0 ++++ ++++
1-x++++++++0−−−−−−−−−−−−−−−−
(2x-11)/(1-x)−−−−−−−−undef++++0−−−−−−−−

Therefore the algebraic fraction is positive only at the integer values between 1 and 5.5:

equation

There are 4 such values.