Solve {l}{text{luatethefunction}f(x)=6x+2}{f(8)=1}

$$\left. \begin{array} { l } { \text { luate the function } f ( x ) = 6 x + 2 } \\ { f ( 8 ) = 1 } \end{array} \right.$$

Solve for f, x

$$x=-\frac{16}{47}\approx -0.340425532$$

$$f=\frac{1}{8}=0.125$$

Solution Steps

Consider the second equation. Divide both sides by 8.

$$f=\frac{1}{8}$$

Consider the first equation. Insert the known values of variables into the equation.

$$\frac{1}{8}x=6x+2$$

Subtract 6x from both sides.

$$\frac{1}{8}x-6x=2$$

Combine \frac{1}{8}x and -6x to get -\frac{47}{8}x.

$$-\frac{47}{8}x=2$$

Multiply both sides by -\frac{8}{47}, the reciprocal of -\frac{47}{8}.

$$x=2\left(-\frac{8}{47}\right)$$

Multiply 2 and -\frac{8}{47} to get -\frac{16}{47}.

$$x=-\frac{16}{47}$$

The system is now solved.

$$f=\frac{1}{8} x=-\frac{16}{47}$$