Solve the Absolute Value Equation: |3x-5| = 12

To solve the equation $\left|3x-5\right|=12$, we split it into two separate equations:

1. $3x-5=12$

2. $3x-5=-12$

For the first equation:

$3x-5=12$

Add 5 to both sides:

$3x=17$

Divide both sides by 3:

$x=5\frac{2}{3}$

For the second equation:

$3x-5=-12$

Add 5 to both sides:

$3x=-7$

Divide both sides by 3:

$x=-2\frac{1}{3}$

Thus, the solutions are $x=5\frac{2}{3}$ and $x=-2\frac{1}{3}$.