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?
Solve the inequality. Then, complete the sentence to describe the solution.
Inequality: 3x ≥ 18
Solution: x ≥ 6
The length of the rectangle must be at least 6 centimeters.
To solve this problem, we need to set up an inequality based on the given information and then solve it.
The length of the rectangle is represented by the variable x. The width of the rectangle is given as 3 centimeters. The formula for the area of a rectangle is A = length * width.
So, the area of the rectangle can be expressed as A = x * 3.
The problem states that the area should be at least 18 square centimeters. This means that the area should be greater than or equal to 18.
Putting it all together, we have the inequality:
x * 3 ≥ 18
Now, let's solve this inequality:
Divide both sides of the inequality by 3 to isolate the variable x:
x ≥ 18 / 3
Simplifying, we get:
x ≥ 6
Therefore, the solution to the inequality is x ≥ 6.
To complete the sentence describing the solution:
The length of the rectangle must be equal to or greater than 6 centimeters in order for the area to be at least 18 square centimeters.
The inequality that describes the problem is: x * 3 ≥ 18.
To solve the inequality, divide both sides of the inequality by 3: x ≥ 6.
Therefore, the solution to the inequality is x ≥ 6.
This means that the length of the rectangle must be equal to or greater than 6 centimeters in order for the area to be at least 18 square centimeters.