Answer
4.5, -9
Work Step by Step
We consider two possible options, since the value within the absolute value can either be positive or negative:
$$ 4x+ 9 = 27 \\ 4x = 18 \\ x=4.5 $$
OR:
$$ 4x+9 =-27 \\ 4x=-36 \\ x=-9$$
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