Question

The perimeter of a rectangle is at most 80 inches. The length of the rectangle is 25 inches. The inequality 80 - 2w ≥ 50 can be used to find w, the width of the rectangle in inches. Solve the inequality and interpret the solution. How will the solution change if the width must be at least 10 inches and a whole number?

Answer 1

The solution to the inequality 80 - 2w ≥ 50 is that the width w of the rectangle must be less than or equal to 15 inches. If w must be at least 10 inches and a whole number, the possible values for w are 10, 11, 12, 13, 14, or 15 inches.

Step-by-step explanation:

To solve the inequality 80 - 2w ≥ 50 and find the width w of the rectangle, let's first move the terms around to isolate w:

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• Subtract 50 from both sides: 80 - 50 ≥ 2w
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• This simplifies to: 30 ≥ 2w
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• Divide both sides by 2: 15 ≥ w

The solution to the inequality means that the width of the rectangle must be less than or equal to 15 inches to keep the perimeter at most 80 inches.

If the width must be at least 10 inches and a whole number, then the possible values for w change. We know that 10 ≤ w ≤ 15. Therefore, the width can be 10, 11, 12, 13, 14, or 15 inches if we restrict it to whole numbers.