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).
