If (x-1)(x+2)<0 , then...?

Answer 1

It must be that x is between 1 and -2, ie, -2 < x < 1.

Edit: Note the "strictly less than" signs. This is due to the same type sign in the question.

The other way to write that is x in (-2, 1)

Answer 2

Break it up this way....A = (x-1) and B = (x+2)
AB < 0 , the A < 0 when B > 0, and A > 0 when B < 0. Test each possibility......try a number line if you find it helpful.

A < 0 , x<1 and B > 0 when x > -2 , so one solution set is: -2 < x < 1 [ e.g., one soln is between -2 and 1 ].

A > 0 , x > 1 and B < 0 , x < -2 ....there is no solution, since you can't have x both > 1 and < -2 at the same time!!

check: TRY SOME VALUES BETWEEN -2 AND 1........... x = -1, A = -2 , B = 1 , A*B = -2 < 0 , etc.....

Solution: -2 < x < 1

Answer 3

-2

Answer 4

(x-1)(x+2)<0
solve
(x-1)(x+2)=0
=> x = 1 OR x= -2
+ x^2 graph => u shaped
< 0 => part of graph below X axis

Ans -2 < x < 1

QED

Answer 5

(x - 1) (x + 2) < 0 means the product is negative.

So, x - 1 may be negative and x + 2 is positive

So, x < 1 and not greater than - 2 to satisfy both the conditions.

Answer 6

well the product of two variables is negative only happens wen
one is positive and othr is negative
therfore
two conditions satisfy this
1) (x-1)<0,(x+2)>0
or
2) (x-1)>0,(x+2)<0
1)x<1, x>-2
comman is {0,-1}
2) no comman is der...so the first condition satisfies da solution
answer is -2

Answer 7

everyone has answered incorrectly. so now complete your question "..then... ?" finish it.