Question 1207257
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How many integers satisfy |x+1| < 4 ?
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Here is even more short reasoning:


<pre>
    The number of integer solutions  of  |x+1| < 4 is the same 
    as the number of integer solutions of   |y| < 4,
    which is obviously 3 + 3 + 1 = 7.
</pre>

Solved.


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Notice that in this problem, &nbsp;they do not ask you to find the set of solutions.
They only ask to determine the number of solutions.


Therefore, &nbsp;in this application, &nbsp;x+1 &nbsp;is a dumb variable and can be replaced by any other variable.


This variable, &nbsp;(x+1), &nbsp;is intently presented in this form to create false associations, 
to distract attention and to motivate a reader to make unnecessary calculations.


Therefore, &nbsp;it is &nbsp;MUCH &nbsp;BETTER &nbsp;to replace it by something more neutral, which does not 
distract attention, does not make false associations and does not motivate to make unnecessary calculations.