If 7 is added to twice a number and this sum is multiplied by 3 , the result is the same as if the number is multiplied by 4 and 9 is added to the product. What is the number?

Let's denote the number as \( x \). Given: 1. If 7 is added to twice a number and this sum is multiplied by 3, the result is the same as if the number is multiplied by 4 and 9 is added to the product. We can set up the equation based on the given information: \[ 3(2x + 7) = 4x + 9 \] Now, let's solve this equation to find the value of \( x \). Solve the equation by following steps: - step0: Solve for \(x\): \(3\left(2x+7\right)=4x+9\) - step1: Expand the expression: \(6x+21=4x+9\) - step2: Move the variable to the left side: \(6x+21-4x=9\) - step3: Subtract the terms: \(2x+21=9\) - step4: Move the constant to the right side: \(2x=9-21\) - step5: Subtract the numbers: \(2x=-12\) - step6: Divide both sides: \(\frac{2x}{2}=\frac{-12}{2}\) - step7: Divide the numbers: \(x=-6\) The solution to the equation is \( x = -6 \). Therefore, the number is -6.