Answer
$b=8$
Work Step by Step
We start with the given equation: $\frac{1}{2}(b-3)=\frac{5}{2}$
We expand the left side of the equation using the distributive property: $\frac{1}{2}b-\frac{3}{2}=\frac{5}{2}$
We multiply both sides of the equation by $2$ to clear the fractions: $b-3=5$
We add $3$ to both sides of the equation: $b-3+3=5+3$
We combine like terms on both sides of the equation: $b=8$
