Step 1 :Translate the problem into a mathematical equation. The statement 'seven times a number' can be represented as \(7x\). 'The difference between seven times a number and 9' can be represented as \(7x - 9\). 'Four times the sum of the number and 5' can be represented as \(4(x + 5)\). The problem states that these two expressions are equal, so the equation is \(7x - 9 = 4(x + 5)\).
Step 2 :Solve the equation for \(x\).
Step 3 :The solution to the equation is \(\frac{29}{3}\), which is the number we are looking for.
Step 4 :Final Answer: The number is \(\boxed{\frac{29}{3}}\).