Chapter 1, Equations and Inequalities - 1.5 Use Problem Solving Strategies and Models - 1.5 Exercises - Quiz for Lessons 1.3-1.5 - Page 40: 4

$k=0.9$

After multiplying both sides by $42$: $28k+12=18k+21\\10k=9\\k=0.9$ Checking by plugging $k=0.9$ into both sides of the original equation: $\frac{2}{3}0.9+\frac{2}{7}=0.6+\frac{2}{7}=\frac{42}{70}+\frac{20}{70}=\frac{62}{70}$ $\frac{3}{7}0.9+\frac{1}{2}=\frac{27}{70}+\frac{35}{70}=\frac{62}{70}$, thus the two sides are equal, and it is a good solution.