Answer
a) $-4$; b) $(-4,\infty)$
Work Step by Step
We are given the functions:
$f(x)=3x+5$
$g(x)=2x+1$
a) Solve the equation $f(x)=g(x)$:
$3x+5=2x+1$
$3x+5-2x=2x+1-2x$
$x+5=1$
$x+5-5=1-5$
$x=-4$
b) Solve the inequality $f(x) \gt g(x)$:
$3x+5\gt 2x+1$
$3x+5-2x\gt 2x+1-2x$
$x+5\gt 1$
$x+5-5\gt 1-5$
$x\gt -4$
The solution set is:
$(-4,\infty)$