The solution set is $(5, \infty)$ .
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). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $ 8x+3 \gt 3(2x+1)+x+5\qquad $ ... distribute, simplify $8x+3 \gt 6x+3+x+5$ $ 8x+3 \gt 7x+8\qquad $ ... $/-3-7x $ $8x-7x \gt >8-3$ $ x \gt 5$ The solution set is $(5, \infty)$ .