Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 40

$x=-3$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{1}{4x+3}=\dfrac{2}{5x-3} ,$ is \begin{array}{l}\require{cancel} 1(5x-3)=2(4x+3) \\\\ 5x-3=8x+6 \\\\ 5x-8x=6+3 \\\\ -3x=9 \\\\ x=\dfrac{9}{-3} \\\\ x=-3 .\end{array}