# Inequalities

• Jun 15th 2009, 11:00 AM
Erghhh
Inequalities
Solve 1/(2x+1) > x/(3x-2)

I've so far done 1/(2x+1) - x/(3x-2) > 0

(2x^2 + 2x -2)/(2x+1)(3x-2) > 0

Now I know that I have to make the top line zero, but it doesn't factorise. Any help?

Thanks.
• Jun 15th 2009, 11:07 AM
stapel
Hint: Quadratic Formula. (Wink)
• Jun 15th 2009, 11:09 AM
craig
Quote:

Originally Posted by Erghhh
Solve 1/(2x+1) > x/(3x-2)

I've so far done 1/(2x+1) - x/(3x-2) > 0

(2x^2 + 2x -2)/(2x+1)(3x-2) > 0

Now I know that I have to make the top line zero, but it doesn't factorise. Any help?

Thanks.

You wouldn't be studying for an FP2 exam would you by any chance ;) ?

Try multiplying both sides by $\displaystyle (2x+1)^2(3x-2)^2$

This gives you $\displaystyle (2x+1)(3x-2)^2 > x(2x+1)^2(3x-2)$

A little rearranging gives you $\displaystyle (2x+1)(3x-2)((3x-2) - x(2x+1)) > 0$

Giving you critical values of $\displaystyle \frac{-1}{2}$ and $\displaystyle \frac{2}{3}$, if you look at the discriminant of the other equation you will notice that it is less than zero, there no real roots.

Using your graphic calculator if you have one, draw the graph of $\displaystyle y = \frac{1}{2x+1} - \frac{x}{3x-2}$, and look to see when it satisfies the inequality.

Hope this helps
• Jun 15th 2009, 11:24 AM
Erghhh
Ahh thank you! I will be doing fp2 on friday, but I found this baby in an fp1 past paper!
• Jun 15th 2009, 11:26 AM
craig
Quote:

Originally Posted by Erghhh
Ahh thank you! I will be doing fp2 on friday, but I found this baby in an fp1 past paper!

Same here, roll on 1.00 Friday afternoon eh ;)

Glad the solution helped