SOLUTION: Solve. 1/x+4>0

Question 137520: Solve.
1/x+4>0
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
1/x+4>0
(1+4x)/x>0
We have a rational inequality.
"To solve a rational inequality, you first find the zeroes (from the numerator) and the undefined points (from the denominator). You use these zeroes and undefined points to divide the number line into intervals. Then you find the sign of the rational on each interval."(purplemath.com)
Find the zero(es) of the numerator:
1+4x=0
4x=-1
x=-1/4
x<>0 because there would be division by 0.
The number line is divide into 3 parts by -1/4 and 0.
Check a number in each part to see if (1+4x)/x is >0 or not.
when x<-1/4 eg. x=-1 then (1+4x)/x=(1+(-4))/-1=-3/-1=3
when -1/4 when x>0 eg. x=1 then(1+4x)/x=(1+4)/1=5
Answer: (-infinity,-1/4)U(0,infinity)
.
Ed
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