SOLUTION: Hi there, I'm having difficulty solving this inequality: 3(t-1)(t-3) > 0 So at first I tried isolating it looks like: 3 > 0 , (t-1) > 0 , (t-3)

SOLUTION: Hi there, I'm having difficulty solving this inequality: 3(t-1)(t-3) > 0 So at first I tried isolating it looks like: 3 > 0 , (t-1) > 0 , (t-3) > 0 In this sense, I

Question 98471: Hi there,
I'm having difficulty solving this inequality:
3(t-1)(t-3) > 0
So at first I tried isolating it looks like:
3 > 0 , (t-1) > 0 , (t-3) > 0
In this sense, I would get:
t > 1 or t > 3
But the right answer is supposed to be t > 3 (Ok, I get this one I think), and t < 1. How did they get the last inequality?
Thank you very much!
Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
3(t-1)(t-3) > 0
It should be t>1 and t>3
Ed
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given inequality

Set the left side equal to zero

Now set each factor equal to zero:

or

or Now solve for t in each case

So our solutions are or

These values make the entire inequality equal to zero. So that means that at or the graph will go from positive to negative (or vice versa). So we must use these points to test the inequality

So now pick any value less than and test the inequality . So lets pick t=0

Plug in t=0

Subtract

Multiply

Since t=0 makes the inequality true, that means everything less than 1 will make the inequality true. So one part of our answer is .

----------------------

Now pick any point in between and . Let's pick t=2

Plug in t=2

Subtract

Multiply

Since t=2 makes the inequality false, that means the possible answer false. So this shows why is not an answer.

----------------------

Now pick any point greater than . Let's pick t=4

Plug in t=0

Subtract

Multiply

Since t=4 makes the inequality true, that means one part of our answer is

That last part is somewhat unnecessary since we already eliminated everything else. However, it is important to see everything that is going on

So our solution is or

Notice if we graph the equation we get

Graph of

and we can clearly see that everything to the left of 1 is greater than zero. Also, we can see that everything to the right of 3 is greater than zero. So our answer is verified.
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