How many different integer values of $x$ satisfy $| x + 6 | < 3$

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Solution

$| x + 6 | < 3$ means $x + 6 < 3$ and $x + 6 > - 3$

$x + 6 < 3 ⟹ x < - 3$
$x + 6 > - 3 ⟹ x > - 9$

$∴$ Values of $x$ satisfying $| x + 6 | < 3$ are $- 8, - 7, - 6, - 5, - 4$ .
Number of integer solutions is $5$ .

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