Question 1207257
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The response from the other tutor shows a standard formal algebraic solution.<br>
Here is another way of solving absolute value equations that is often easier than the formal algebraic solution.<br>
The expression<br>
{{{abs(x-a)<b}}}<br>
can be interpreted as meaning that the difference between x and a is less than b.<br>
In this problem....<br>
{{{abs(x+1)<4}}} --> {{{abs(x-(-1))<4}}}<br>
This says that the difference between x and -1 is less than 4, where x is an integer. In other words, if we look at a number line, x can be any integer whose distance from -1 is less than 4.<br>
3 units to the right of -1 is -1+3=2; 3 units to the left of -1 is -1-3=-4.  So x can be any integer from -4 to +2 inclusive; that is 7 integers.<br>
Or, the previous paragraph more simply: the integers that satisfy the inequality are -1, plus 3 integers either side of -1, for a total of 1+3+3 = 7.<br>