SOLUTION: Solve the inequality x^2-5x+6>0. State the solution set using interval notation and graph it. Any help is greatly appreciated.

Question 7125: Solve the inequality x^2-5x+6>0. State the solution set using interval notation and graph it. Any help is greatly appreciated.
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
First, you would factor the trinomial on the left side of the >. We'll have to get that inequality to say something like (x � ?)(x � ?) > 0. So, what times what = 6 that has a sum or a difference of -5? It turns out to be

By looking at the factored inequality, you can pick out the "solutions" to be 2 and 3. Since its an inequality, the true solutions will be a range in the number line. The 2 and the 3 are just your critical points. Since the inequality is a >, you would draw open circles at 2 and at 3 on the number line.

The two open circles divide the number line into three intervals: (-∞,2),(2,3) and (3,∞). So, which of these intervals is a solution to your inequality? We'll have to attempt a series of trial and error.

Let's take the (-∞,2) and choose a random number in that range. Let's pick 0 because it seems easiest, and plug it into the inequality. (0 - 2)(0 - 3) ?> 0. It turns out that 6 > 0 which is true. Just because the 0 passed the inequality, so will ALL values in the interval (-∞,2). So, (-∞,2) is a solution.

Let's take the (2,3) and choose a random number in that range, say 2.5, smack in the middle. Let's plug it in: (2.5 - 2)(2.5 - 3) ?> 0 ---> (0.5)(-0.5) ?> 0 fails because the left side gave us a negative number, definitely not greater than 0. Just because the 2.5 failed, so will ALL the other values in the range (2,3). So (2,3) is not a solution to the inequality.

What about the (3,∞)? Let's pick the value 4 and plug it in to see if it will work. (4 - 2)(4 - 3) ?> 0 ---> (2)(1) ?> 0 turns out to be true. So, just because the 4 passed the inequality and is in the range (3,∞), (3,∞) is a solution set of your inequality.

So two intervals make up the solution to your inequality: (-∞,2) and (3,∞). They might even want you to write it as (-∞,2) U (3,∞).
RELATED QUESTIONS
I submitted this wrong the correction is, Solve each inequality. State the solution... (answered by AnlytcPhil)

Please help! Solve each compound inequality. State the solution set using interval... (answered by jim_thompson5910)

Could some one help me understand this problem? The instructions are to solve the... (answered by venugopalramana)

solve the inequality,state the solution set using interval notation and graph the... (answered by stop12345now)

Please help me solve the inequality and determine the graph of the solution set for... (answered by chessace)

Solve each inequality. State the solution set using interval notation and graph the... (answered by mathmaven53)

please help me solve these problems thank you Solve the inequality. State the... (answered by solver91311)

Thank you in advance for helping me with the following problems. I am struggling with... (answered by stanbon)

Can you please help me with this? ) Solve the inequality and state the solution set... (answered by mukhopadhyay)