M28-46

I'm happy to answer your doubt, regardless of the question. I will answer it as we solve inequality.

What does it mean X(X-2)>0 ? Let's put it in simple way.

We have TWO number A & B are multiplied and result Bigger than 0. When does Happen?

From NUMBER PROPERTIES:

Case 1: A = positive & B= positive ............ A * B >0

Case 2: A =negative & B= negative ............ A * B >0

Let look to our inequality :

X(X-2)>0

Put: A=X & B= X-2

Using cases mentioned above let's analyze our inequality:

Case 1:

X (X-2)>0.......... Remember A & B positive means A >0 & B>0

X>0 & X-2>0 then X>2 ....... Can you come up with example that satisfy that X>0 & X>2 in same time???Answer:YES we can. Any number BIGGER than 2 does so

CASE 1 yields that X>2

Case 2

X (X-2)>0.......... Remember A & B negative means A <0 & B<0

X<0 & X-2<0 then X<2........Can you come up with example that satisfy that X<0 & X<2 in same time???Answer:YES we can. Any number SMALLER than 0 does so.

CASE 2 yields that X<0

From above Cases we can conclude FINALLY that: TO SATISFY the Inequality:

Either X<0 or X>2................NOTICE that when we combine TWO CASES, we use 'Either......OR......'

You can check number if you are in doubt.

I will expand my explanation about how to solve if you face this question:

X (X-2)<0

From NUMBER PROPERTIES:

Case 1: A = positive & B= negative ............ A * B <0

Case 2: A =negative & B= positive ............ A * B <0

Put: A=X & B= X-2

Using cases mentioned above let's analyze our inequality:

Case 1:

X (X-2)<0.......... Remember A = positive means A >0 & B=negative means B<0

X>0 & X-2<0 then X<2 ....... Can you come up with example that satisfy that X>0 & X<2 in same time???Answer:YES we can. Any number BIGGER than 0
& SMALLER than 2. We can put mathematically as 0<X<2. For example X=3/2

CASE 1 yields that 0<X<2


Case 2

X (X-2)>0.......... Remember A = negative means A < 0 & B=positive means B>0

X<0 & X-2>0 then X>2........Can you come up with example that satisfy that X<0 & X>2 in same time???Answer:NO, we can NOT. It means that we need a number that is negative and positive in same time. Can you find it?

CASE 2 yields no solution


From above Cases we can conclude FINALLY that: TO SATISFY the Inequality:

0<X<2

Check numbers if you want.