Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 37

$x=6$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{-1}{x-7}=\dfrac{5}{x-1} ,$ is \begin{array}{l}\require{cancel} -1(x-1)=5(x-7) \\\\ -x+1=5x-35 \\\\ -x-5x=-35-1 \\\\ -6x=-36 \\\\ x=\dfrac{-36}{-6} \\\\ x=6 .\end{array}