Final answer:
The expression representing the total cost of the fence including the gate is 43x + 128, where 'x' is the length of the fence in feet, excluding the gate.
Step-by-step explanation:
Shannon is putting a fence around the garden, with a 3 feet wide gate for which the cost is $128. To express the total cost of the fence including the gate, we need to calculate the cost per foot of the fence, which is $43, and then add the cost of the gate. Let's denote the total length of the fence required, excluding the gate, as 'x' feet. The cost of the fence would be 43x dollars (cost per foot multiplied by the number of feet).
The complete expression to represent the total cost of the fence including the gate is 43x + 128. Here, 43x represents the total cost of the fence per foot, and 128 represents the cost of the gate.