Question

I don’t understand this problem math solve for proportion math

Answer 1

We want to solve for x

`(x-9)/(3)=(56)/(x+4)`

Solution

`\begin{gathered} (x-9)/(3)=(56)/(x+4) \\ \text{cross multiply} \\ (x-9)(x+4)=3*56 \\ x(x+4)-9(x+4)=168 \\ x^2+4x-9x-36=168 \\ x^2-5x-36=168 \\ x^2-5x-36-168=0 \\ x^2-5x-204=0 \end{gathered}`

We now have a quadratic equation

We therefore solve by factorization method

`\begin{gathered} x^2-5x-204=0 \\ x^2-17x+12x-204=0 \\ x(x-17)+12(x-17)=0 \\ (x-17)(x+12)=0 \\ x-17=0 \\ x=17 \\ or \\ x+12=0 \\ x=-12 \\ \\ x=17,-12 \end{gathered}`

The final answer is x = 17 or x = -12