Question

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

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Answer 1

$|x-3|$ is the distance between x and 3. The set of integers which satisfy the condition $|x-3|$ $>$ 5 or
whose distance from 3 is more than 5 units will be

Similarly$|x+1|$ $\le$ 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 the first set]