# Solve the following inequality

• Feb 20th 2011, 05:19 AM
hoanghai549
Solve the following inequality
(3a+7)/(a+4) >= 0

• Feb 20th 2011, 05:35 AM
Plato
Quote:

Originally Posted by hoanghai549
(3a+7)/(a+4) >= 0

You want to insure that both of $\displaystyle 3a+7\ge0~\&~a+4>0$ are true
or both $\displaystyle 3a+7\le0~\&~a+4<0$ are true.
• Feb 20th 2011, 05:41 AM
hoanghai549
So It means I have to solve the two above conditions or just use the one thing ?
• Feb 20th 2011, 05:52 AM
Plato
Quote:

Originally Posted by hoanghai549
So It means I have to solve the two above conditions or just use the one thing ?

There will be two different intervals in the solution set.
So solve both and unite.
• Feb 20th 2011, 05:54 AM
hoanghai549
• Feb 20th 2011, 07:14 AM
deleted
• Feb 20th 2011, 03:45 PM
Plato
Quote:

Originally Posted by hoanghai549
(3a+7)/(a+4) >= 0

Look at the numerator and the denominator.
If both have the same sign then the inequality is true.
It is easy to see that if $\displaystyle a<-4$ then both are negative.
If $\displaystyle a\ge -\frac{7}{3}$ then both are non-negative.

Write the solution set as $\displaystyle (-\infty,-4)\cup\left[-\frac{7}{3},\infty\right)$.

There is no complicated calculation necessary.