Question

What is the solution of {3x + 8}/{x - 4} > 0 ?

a) ( x < -8/3 ) or ( x < 4 )
b) ( x > -8/3 ) or ( x < 4 )
c) ( x < -8/3 ) or ( x > 4 )
d) ( x > -8/3 ) or ( x > 4 )

Answer 1

Option A). The solution to the inequality {3x + 8}/{x - 4} > 0 is ( x < -8/3 ) or ( x < 4 ).

Step-by-step explanation:

The solution to the inequality {3x + 8}/{x - 4} > 0 can be found by analyzing the signs of the numerator and the denominator.

1. If the numerator is positive and the denominator is positive, then x < -4. This is because any positive number divided by a positive number is positive.
2. If the numerator is negative and the denominator is negative, then x < -8/3 . This is because any negative number divided by a negative number is positive.

Therefore, the solution to {3x + 8}/{x - 4} > 0 is a) ( x < -8/3 ) or ( x < 4 ). Answer choice a is correct.