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

How many integer values of x are there such that:

Process the inequality algebraically:

and note that:

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:

There are 4 such values.