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). --- $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 $(3, 5)$ .