Question

Find the number of integers satisfying the condition |x-3| $>$ 5 and |x + 1 | $\le$ 4

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Answer 1

Ix - 3|is the distance between x and 3. The set of integers which satisfy the condition Ix - 3| $>$ 5 or

whose distance from 3 is more than 5 units will be

Similarly Ix + 1| $<$ 4 means set of all integers which are less than or equal to 4 units from '-1'. They are

The numbers common are -5, -4, -3. [-2 is not part of 1st set]