Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 43

$x=\dfrac{9}{2}$

Multiplying both sides by the $LCD= 4 ,$ the value of the variable that satisfies the given equation, $ \dfrac{x-1}{2}-1=\dfrac{3}{4} ,$ is \begin{array}{l}\require{cancel} 2(x-1)-4(1)=1(3) \\\\ 2x-2-4=3 \\\\ 2x=3+2+4 \\\\ 2x=9 \\\\ x=\dfrac{9}{2} .\end{array}