Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises - Page 120: 104

$x=\dfrac{1}{3}$

The given inequality, $ |6x-2|=0 ,$ is equivalent to \begin{array}{l}\require{cancel} 6x-2=0 .\end{array} Using the properties of equality, the solution to the equation above is \begin{array}{l}\require{cancel} 6x=2 \\\\ x=\dfrac{2}{6} \\\\ x=\dfrac{\cancel{2}}{\cancel{6}^3} \\\\ x=\dfrac{1}{3} .\end{array}