Solve the inequality for \( w \). \[ 5(3 w+7)>6 w+17 \] Simplify your answer as much as possible. \begin{tabular}{|l|c|c|c|}\hline\( \square \) & \( \square>\square \) & \( \square \leq \square \) \\ \( \square \geq \square \) & \( \frac{\square}{\square} \) & \( \square \frac{\square}{\square} \) \\ \hline & \( \times \) & 5 \\ \hline\end{tabular}

To solve the inequality \( 5(3w + 7) > 6w + 17 \), we start by distributing the 5 on the left side: \[ 15w + 35 > 6w + 17 \] Next, we isolate the variable \( w \) by moving all terms involving \( w \) to one side and constant terms to the other side. Subtract \( 6w \) from both sides: \[ 15w - 6w + 35 > 17 \] This simplifies to: \[ 9w + 35 > 17 \] Next, subtract 35 from both sides: \[ 9w > 17 - 35 \] This simplifies to: \[ 9w > -18 \] Now, divide both sides by 9: \[ w > -2 \] Thus, the solution to the inequality is: \[ w > -2 \] In the box format you provided, this could be represented as: | | > | | |---|---|---| | | \( w \) | \( -2 \) |