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Laura is drawing a rectangle. The width will be 3centimeters3\,\text{centimeters}, and the area will be at least 18square centimeters18\,\text{square centimeters}. Let xx represent the length of the rectangle. Which inequality describes the problem?\newlineChoices:\newline(A) 3x183x \leq 18\newline(B) 3x183x \geq 18\newlineSolve the inequality. Then, complete the sentence to describe the solution. The rectangle will be at least ____\_\_\_\_ centimeters long.

Full solution

Q. Laura is drawing a rectangle. The width will be 3centimeters3\,\text{centimeters}, and the area will be at least 18square centimeters18\,\text{square centimeters}. Let xx represent the length of the rectangle. Which inequality describes the problem?\newlineChoices:\newline(A) 3x183x \leq 18\newline(B) 3x183x \geq 18\newlineSolve the inequality. Then, complete the sentence to describe the solution. The rectangle will be at least ____\_\_\_\_ centimeters long.
  1. Identify formula: Step 11: Identify the formula for the area of a rectangle. The formula is Area=width×length\text{Area} = \text{width} \times \text{length}. Here, width=3cm\text{width} = 3 \, \text{cm} and Area18sq cm\text{Area} \geq 18 \, \text{sq cm}.
  2. Substitute values: Step 22: Substitute the known values into the area formula to form an inequality. 183x18 \leq 3x.
  3. Solve inequality: Step 33: Solve the inequality for x. Divide both sides by 33 to isolate xx. 18÷3x18 \div 3 \leq x, so x6x \geq 6.

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