# How do you prove that the limit of (3x+2)=8  as x approaches 2 using the epsilon delta proof?

$\delta \left(\epsilon\right) = \frac{\epsilon}{3}$
$\left\mid f \left(x\right) - L \right\mid = \left\mid 3 x + 2 - 8 \right\mid = 3 \left\mid x - 2 \right\mid$
Then if we choose $\delta = \frac{\epsilon}{3}$
$\left\mid x - 2 \right\mid < \delta = \setminus \setminus \implies \setminus \setminus \left\mid f \left(x\right) - L \right\mid = 3 \left\mid x - 2 \right\mid < 3 \delta = \epsilon$