Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 184: 69

$x\gt\dfrac{9}{2}$

Using the Distributive Property and the properties of inequalities, the solution to the given inequality, $ -12\gt-4(x-1)+2 ,$ is \begin{array}{l}\require{cancel} -12\gt-4x+4+2 \\\\ 4x\gt4+2+12 \\\\ 4x\gt18 \\\\ x\gt\dfrac{18}{4} \\\\ x\gt\dfrac{\cancel{2}\cdot9}{\cancel{2}\cdot2} \\\\ x\gt\dfrac{9}{2} .\end{array}