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The length of a rectangle is 3x - 5. Its width is 10cm. For which values of x is the area of the rectangle larger than the perimeter?

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Final answer:

To find the values of x for which the area of the rectangle is larger than the perimeter, we can use the formulas for area and perimeter of a rectangle.

Step-by-step explanation:

To find the area and perimeter of the rectangle, we need to use the formulas:

Area = length * width

Perimeter = 2 * (length + width)

The length of the rectangle is given as 3x - 5, and the width is given as 10cm. We want to find the values of x for which the area is greater than the perimeter:

Area > Perimeter

Substituting the given values, we have:

(3x - 5) * 10 > 2 * ((3x - 5) + 10)

Expanding this equation, we get:

30x - 50 > 6x + 10

Combining like terms, we have:

24x > 60

Dividing both sides by 24, we get:

x > 2.5

Therefore, for values of x greater than 2.5, the area of the rectangle will be larger than the perimeter.

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