Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 13

$x\lt\dfrac{5}{2}$

Using the properties of inequality, the solution to the given inequality, $ -4x+6\gt-2x+1 ,$ is \begin{array}{l}\require{cancel} -4x+2x\gt1-6 \\\\ -2x\gt-5 \\\\ x\lt\dfrac{-5}{-2} \\\\ x\lt\dfrac{5}{2} .\end{array}