Question

a valentine’s movie night costs $9 per ticket plus a $6 online fee. you want to spend at most $60. what is the inequality for the problem? what is the solution? how many tickets can you buy? write the answer as a sentence.

Explanation:

Step1: Define variable & set inequality

Let $x$ = number of tickets. Total cost is $9x + 6$, which must be ≤ 60.
$$9x + 6 \leq 60$$

Step2: Subtract 6 from both sides

Isolate the term with $x$.
$$9x + 6 - 6 \leq 60 - 6$$
$$9x \leq 54$$

Step3: Divide by 9 to solve for x

Solve for the maximum $x$.
$$\frac{9x}{9} \leq \frac{54}{9}$$
$$x \leq 6$$

Answer:

1. The inequality is $9x + 6 \leq 60$
2. The solution is $x \leq 6$
3. You can buy at most 6 tickets.