Problem
Solve the inequality for $v$. \[ -23+7(5-v) \leq-3(v+4) \] Simplify your answer as much as possible.
Solution
Step 1 ：Distribute the 7 on the left side and the -3 on the right side of the inequality to get \(-23 + 35 - 7v \leq -3v - 12\).
Step 2 ：Combine like terms to get \(12 - 7v \leq -3v - 12\).
Step 3 ：Isolate the variable $v$ on one side of the inequality to get \(v = 6\).
Step 4 ：Check if this value satisfies the original inequality. Substituting $v = 6$ into the original inequality, we find that it holds true.
Step 5 ：Thus, the solution to the inequality is \(v \leq 6\).
Step 6 ：Final Answer: \(v \leq \boxed{6}\)
