Answer:
B
Explanation:
5(x-2)(x+4)>0 can be simplified as (x-2)(x-4)>0, you just divide both sides by 5.
You can temporarily treat the inequality sign as an equals sign. So in a regular equation like (x-2)(x+4)=0, we can split this up into two different equations:
(x-2)=0 and (x+4)=0
This gets you x=2 and x=-4. However, since there is not actually an equals sign in this equation, you have to find another way to figure out which way the inequality sign goes for both x-values. But by this point you already know the x-values that will be employed in the inequality!
Now when you look at A, B, C, and D, you can eliminate options:
The only options that include an inequality with 2 and -4 are A and B. So it has to be one of the two.
Proceed by plugging in possibilities for each of the solutions given.
Try A: x>-4 and x<2
-3>-4 so I will use -3 as the x-value:
5(-3-2)(-3+4)>0
5(-5)(1)>0
-25>0
This is not true so A is not the answer.
Try B: x<-4 or x>2
-5<-4 so I will use -5 as the x-value:
5(-5-2)(-5+4)>0
5(-7)(-1)>0
35>0
This is true so B could be the answer. Now let's try the second x-value possibility, when x>2.
3>2 so I will use 3 as the x-value:
5(3-2)(3+4)>0
5(1)(7)>0
35>0
Also true, so B is correct.