Question

laura is drawing a rectangle. the width will be 3 centimeters, and the area will be at least 18 square centimeters. let x represent the length of the rectangle. which inequality describes the problem? 3x ≤ 18 3x ≥ 18 solve the inequality. then, complete the sentence to describe the solution. the rectangle will be at least centimeters long.

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. Here, width = 3 cm and length = $x$ cm, so $A = 3x$.

Step2: Set up the inequality

Since the area will be at least 18 square - centimeters, we use the $\geq$ symbol. So the inequality is $3x\geq18$.

Step3: Solve the inequality

Divide both sides of $3x\geq18$ by 3. We get $\frac{3x}{3}\geq\frac{18}{3}$, which simplifies to $x\geq6$. So the rectangle will be at least 6 centimeters long.

Answer:

1. B. $3x\geq18$
2. 6