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Natalka [10]
2 years ago
15

Solve: x+2/x-4<0 O _4 O -2 -2 -4

Mathematics
1 answer:
sammy [17]2 years ago
7 0

Answer:

-2<x<4

Step-by-step explanation:

For \frac{x+2}{x-4} < 0, note that either the numerator or denominator is positive and the other must be negative for this inequality to be satisfied.

This means x+2>0 and x-4<0 or x+2<0 and x-4>0.

Lets look at the first scenario (x+2>0 and x-4<0)

x+2>0 and x-4<0

x>-2 and x<4

This means that -2<x<4.

Let’s look at the other scenario (x+2<0 and x-4>0)

x+2<0 and x-4>0

x<-2 and x>4

This means that x must be <-2 and >4 simualtaneously, which is impossible.

Therefore, this only occurs when -2<x<4.

I hope this helps! :)

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