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07-02-2024
Mathematics

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Consider the shape with dimensions given in the diagram below (measured in inches). A figure is formed from three rectangles. A rectangle with sides x and 3 is shown to have area 3 x. That rectangle sits on top of a second rectangle with area shown as, in parentheses, x plus 2, end parentheses, times x. It is placed next to the third rectangle, with sides 4 and x plus 2. Its area is shown to be 4 x plus 8. The number inside of each rectangle represents the area of that region. The total area is 78 square inches. Determine the value of x.

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