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 $\$ 12$ ?
\[
\begin{array}{ll}
\text { A } & 6+3 x \leq 12 \\
\text { B } & 6-3 x \leq 12 \\
\text { C } & 12 \leq 6+3 x \\
\text { D } & 12 \leq 6-3 x
\end{array}
\]

Answer

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Answer

$\boxed{x \leq 2}$

Steps

Step 1 ：Find the inequality representing the total cost: $6 + 3x \leq 12$

Step 2 ：Solve the inequality: $x \leq 2$

Step 3 ：$\boxed{x \leq 2}$