First, we begin with #1/2root(3)(x-7)+3=2#. This looks messy, but it is actually pretty simple, as long as we go step by step. Our goal is to isolate #x#. First, we should subtract #3# on both sides. That would give us
#1/2root(3)(x-7)=-1#.
Now, we divide by #1/2# on each side. This is equivalent to multiplying by #2# on both sides, which either way gives us
#root(3)(x-7)=-2#.
To get rid of the #root(3)#, we simply apply its inverse, which is cubing. So we cube both sides, and we get
#(root(3)(x-7))^3=(-2)^3=x-7=-8#.
We just add #7#, and we are left with
#x=-1#.
To confirm we are correct we should double check our work, by confirming that when #x=-1#, the earlier equation is still equal to #2#.
#1/2root(3)((-1)-7)+3=2# becomes #1/2root(3)(-8)+3=2#, or #1/2*-2+3=2#. Now, #1/2# multiplied by #-2# is #-1#, and #-1+3# is equal to #2#. Therefore, we were correct, and #x=-1#. Good job!
