# How To Solve This Inequality?

• Sep 13th 2009, 11:53 PM
AlphaRock
How To Solve This Inequality?
6x+4 <= x-6 < 4x + 10

My work:
6x+4 <= x-6 < 4x + 10
6x+4+6 <= x < 4x+10+6
6x+10 <= x < 4x+16

Not really sure how to finish this...
• Sep 14th 2009, 02:51 AM
Finley
It's much easier if you break it into two separate inequations and then bring the solutions together at the end if necessary:

$6x+10 < x$
$x < 4x+16$

Can you finish it off now?
• Sep 14th 2009, 02:52 AM
Amer
Quote:

Originally Posted by AlphaRock
6x+4 <= x-6 < 4x + 10

My work:
6x+4 <= x-6 < 4x + 10
6x+4+6 <= x < 4x+10+6
6x+10 <= x < 4x+16

Not really sure how to finish this...

solve it like this

6x+4<=x-6

5x <= -10

x <= -2 this the first interval

x-6 < 4x+10

3x > -16

x > -16/3 now find the intersection of the two intervals (-infinity , -2] and (-16/3 , infinity)