Question

1. pizzas cost $12 each. zach wants to spend between $72 and $108, inclusive. create and solve a compound inequality to determine how many basketballs josh can buy. graph your solution, and then write your answer as a sentence.

Explanation:

Step1: Define the variable

Let \( n \) be the number of pizzas. The cost of \( n \) pizzas is \( 12n \) dollars.

Step2: Set up the compound inequality

Zach wants to spend between \$72 and \$108 (inclusive), so we have the inequality:

$$ 72 \leq 12n \leq 108 $$

Step3: Solve the inequality

Divide all parts of the inequality by 12:

$$ \frac{72}{12} \leq \frac{12n}{12} \leq \frac{108}{12} $$

Simplify each part:

$$ 6 \leq n \leq 9 $$

Step4: Interpret the solution

The number of pizzas Zach can buy is between 6 and 9, inclusive. To graph this, we draw a number line, mark the points 6 and 9, and shade the region between them (including the endpoints).

Answer:

Zach can buy between 6 and 9 pizzas, inclusive. The compound inequality solution is \( 6 \leq n \leq 9 \) (where \( n \) is the number of pizzas), and the graph is a number line with closed circles at 6 and 9 and shading in between.