Question 65355
Solve for x:

a)y-x=6
y-y-x=6-y
-x=6-y
-1(-x)=-1(6-y)
x=-6+y <---this is fine
x=y-6 <---some teachers don't want leading negatives if possible, if that's the case switch the order.
b)1/x+7>-3
If this is what your mean:
{{{1/x+7>-3}}}
{{{1/x+7+3>-3+3}}}
{{{1/x+10>0}}}  Now solve this like it's an equation.
{{{1/x=-10}}}
{{{(1/x)^(-1)=(-10)^(-1)}}}
{{{x=-1/10}}} <---That's a critical number along with 0, because it's undefined at 0.
(-infinity,-1/10) or (-1/10,0) or(0,infinity)
For (-infinity,-1/10) test -1
{{{1/-1+7>-3}}}
{{{-1+7>-3}}}
{{{6>-3}}} True, accept this interval.
For (-1/10,0) test -1/11
{{{1/(-1/11)+7>-3}}}
{{{-11+7>-3}}}
{{{-4>-3}}}  <---false reject this interval
For (0,infinity) test 1
{{{1/1+7>-3}}}
{{{1+7>-3}}}
{{{8>-3}}} <--true accept this interval
The solution is: (-infinity,-1/10)U(0,infinity)
Happy Calculating!!!