Question

write a related function for 6x - 3x - 2 = 7.

Explanation:

Step1: Simplify the left side

First, combine like terms in \(6x - 3x-2\). \(6x - 3x=3x\), so the equation becomes \(3x - 2 = 7\).

Step2: Form the related function

To write a related function, we set the left - hand side minus the right - hand side equal to \(y\) (or \(f(x)\)). So, \(y=3x - 2-7\), which simplifies to \(y = 3x-9\) (or \(f(x)=3x - 9\)). We can also think of it as moving all terms to one side of the equation to form a function. Starting from \(6x - 3x-2 = 7\), we can rewrite it as \(6x-3x - 2-7 = 0\), and then simplify the left - hand side. \(6x-3x=3x\) and \(-2 - 7=-9\), so the function is \(f(x)=3x - 9\) (or \(y = 3x-9\)).

Answer:

\(f(x)=3x - 9\) (or \(y = 3x-9\))