Question

I got this problem wrong. Can someone help me correct it?

Answer 1

x < 1/2 or x < - 4/3

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