What is the best approach regarding solving multivariable inequalities? Thanks
If x + y + z > -, is z >1?
1. z> x + y + 1
2. x + y + 1 < 0
If x + y + z > -, is z >1?
1. z> x + y + 1
2. x + y + 1 < 0
one difference between inequalities and equations is the sign => instead of = we may have <, >, =<, >= so four alternativestonebeeze wrote:What is the best approach regarding solving multivariable inequalities? Thanks
If x + y + z > - ..., is z >1?
1. z> x + y + 1
2. x + y + 1 < 0
x+y+z>- ... can be rewritten as x+y+z+... >0
then (1) z>x+y+1 OR z-x-y-1>0 [+] x+y+z+...>0 is equivalent to 2z-1+...>0 and z>1/2-...
so depending on (...) z can be less or greater than 1 or even equal to 1 Not Sufficient
(2) x+y+1<0 OR -x-y-1>0 [+] x+y+z+...>0 is equivalent to z-1+...>0 and z>1-...
depending on (...) z can be less or greater than 1 or even equal to 1 Not Sufficient
Combining st (1&2) we get z-x-y-1>0 [-] -x-y-1>0 and z>0, so z can be again less, greater or equal to 1 Not Sufficient
Our answer is defined with the value and sign of (...)
If (...)<-1/2 then pick D
If (...)=<0 then pick B
If (...)>0 then pick E
so what's (...)?
