Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 28

$x=111$

Using cross-multiplication and the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{x-6}{7}=\dfrac{x+9}{8} ,$ is \begin{array}{l}\require{cancel} 8(x-6)=7(x+9) \\\\ 8x-48=7x+63 \\\\ 8x-7x=63+48 \\\\ x=111 .\end{array}