Step 1 :The problem states that a 20-inch board is cut into three pieces. The first piece is x inches long, the second piece is 4 times as long as the first piece, and the third piece is 5 times as long as the first piece. This means that the total length of the board is the sum of the lengths of the three pieces.
Step 2 :We can set up an equation to represent this relationship: \(x + 4x + 5x = 20\)
Step 3 :Solving this equation gives us \(10x = 20\)
Step 4 :Dividing both sides of the equation by 10 gives us \(x = 2\)
Step 5 :Final Answer: The length of the first piece is \(\boxed{2}\) inches.