Problem
Solving \& graphing equivalent inequalities with negative $x$. Patricia has $\$ 12$ to spend at an arcade. The arcade charges $\$ 6$ admission and $\$ 3$ per hour to play as many games as she wants. Which inequality can be used to find any possible number of hours, $x$, Patricia can play games without spending more than $\$ 12$ ? \[ \begin{array}{ll} \text { A } & 6+3 x \leq 12 \\ \text { B } & 6-3 x \leq 12 \\ \text { C } & 12 \leq 6+3 x \\ \text { D } & 12 \leq 6-3 x \end{array} \]
Solution
Step 1 ：Find the inequality representing the total cost: \(6 + 3x \leq 12\)
Step 2 ：Solve the inequality: \(x \leq 2\)
Step 3 ：\(\boxed{x \leq 2}\)
