Answer
$(3, 5)$
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
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$6 \lt x+3 \lt 8 \qquad $ ... add $(-3)$ to all
$6-3 \lt x+3-3 \lt 8-3$
$3 \lt x \lt 5$
... both interval borders are excluded
The solution set is $(3, 5)$ .
