Answer
$(0,\infty)$
Work Step by Step
$4(2x+1)\gt4$
Solve for x. Divide both sides of the equation by 4.
$\frac{4(2x+1)}{4}\gt4\div4$
$2x+1\gt1$
Subtract 1 from each side then divide by 2.
$2x+1-1\gt1-1$
$2x\gt0$
$2x\div2\gt0\div2$
$x\gt0$
In interval notation this is written as
$(0,\infty)$
where ( indicates that the solution set for x approaches, but does not include, 0.