Igot this problem wrong. can someone me correct it?

x <  1/2 or x  <  - 4/3

Step-by-step explanation:

Here, the given expression is:

-( 2 x - 1) ( 3 x + 4 ) >  0

⇒  ( 2 x - 1) ( 3 x + 4 ) <  0

Now, it implies:  ( 2 x - 1) < 0 or  ( 3 x + 4 ) <  0

Case 1:    ( 2 x - 1) < 0

⇒2 x  -1 + 1 < + 1   ( adding 1 on both sides)

or, 2 x < 1  

Now, divide both sides by 2, we get:

or  x < 1/2  

Case 2:    (3 x + 4) < 0

⇒ 3 x +  4 - 4   < - 4   ( adding (-4)  on both sides)

or,  3 x <  - 4

Now, divide both sides by 3, we get:

x <  -4 / 3

Hence, x is  either LESS THAN 1/2 or x is  LESS THAN - 4/3