Final answer:
The perimeter of a rectangular garden with a width of 2x-5 and a length of 3x+1 is given by the expression 10x - 8, calculated using the formula P = 2l + 2w.
Step-by-step explanation:
To find the perimeter of a rectangular garden with a width of 2x-5 and a length of 3x+1, we use the formula for the perimeter of a rectangle, which is:
P = 2l + 2w
Where 'P' is the perimeter, 'l' is the length, and 'w' is the width of the rectangle.
Plugging in the given expressions for length and width:
P = 2(3x + 1) + 2(2x - 5)
Now, simplify the equation by distributing the 2:
P = 2 × 3x + 2 × 1 + 2 × 2x - 2 × 5
P = 6x + 2 + 4x - 10
Combine like terms:
P = (6x + 4x) + (2 - 10)
P = 10x - 8
Thus, the perimeter of the rectangular garden is given by the expression 10x - 8, where 'x' can be any real number.