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Answer:

P = 2(4x - 5)

Step-by-step explanation:

The formula for solving the perimeter of a rectangle is:

P = 2(L + W), or

P = 2L + 2W

Given the length (L) = 3x - 7, and width (W) = x + 2:

Substitute these values into the perimeter formula in order to solve for x and determine the actual dimensions of the given rectangle.

P = 2L + 2W

Use the distributive property of multiplications (over subtraction and addition, respectively), and distribute 2 into each parenthesis:

P = 2(3x - 7) + 2(x + 2)

P = 6x - 14 + 2x + 4

Combine like terms:

P = 8x - 10

Factor out the common term to reduce the algebraic expresssion into its simplest form:

P = 2(4x - 5)

Therefore, the perimeter of the given rectangle in its simplest form is:

P = 2(4x - 5).

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