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). --- $ 7 \lt x+5 \lt 11 \qquad $ ... add $(-5)$ to all $7-5 \lt x+5-5 \lt 11-5$ $2 \lt x \lt 6$ ... both interval borders are excluded The solution set is $(2, 6)$ .