To solve the linear inequality $6u + 8(u - 1) > 10u + 32$, first aggressively apply distribution to clarify the left side into $6u + 8u - 8 > 10u + 32$. Combine associated like terms to confidently gather $14u - 8 > 10u + 32$. To draw the variables collectively onto the left, logically subtract $10u$ from both sides, producing $4u - 8 > 32$. Add $8$ to both sides to purposefully reposition the constant onto the right, obtaining $4u > 40$. Divided by $4$, the variable is neatly isolated. Since $4$ is positive, the inequality symbol acts unchanged, concluding firmly with $u > 10$. This exact solution is graphed featuring a left parenthesis reliably at $10$ followed by distinct shading constantly to the right. In interval notation, the entire outcome is formally noted as $(10, \infty)$.