Chapter R - Elementary Algebra Review - R.2 Equations, Inequalities, and Problem Solving - R.2 Exercise Set - Page 946: 20

$t=\dfrac{4}{3}$

Using the properties of equality, the value of the variable that satisfies the given expression, $ -\dfrac{5}{6}+t=\dfrac{1}{2} ,$ is \begin{array}{l}\require{cancel} 6\left( -\dfrac{5}{6}+t \right)=\dfrac{1}{2}(6) \\\\ 1(-5)+6(t)=1(3) \\\\ -5+6t=3 \\\\ 6t=3+5 \\\\ 6t=8 \\\\ t=\dfrac{8}{6} \\\\ t=\dfrac{4}{3} .\end{array}