You can put this solution on YOUR website! You just don't want the denominator to be zero.
So we set 4x+7 to zero and solve for x:
4x+7 = 0
4x = -7
x = -7/4
this is the only value that x can't take
so the domain is:
(-oo, -7/4) U (-7/4, +oo)
where oo indicates infinity