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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:
Therefore the algebraic fraction is positive only at the integer values between 1 and 5.5:
There are 4 such values.