# inequalities

• Sep 16th 2008, 04:44 PM
xian791
inequalities
2(x-3)-3(x+2)<5

i seriously don't know where to start. I was thinking of putting 5 on the other side, but i would be stuck from there.

P.S. if i do find the numbers for instance, 3,-3, 8. I would have to graph them on a number line and see if its a positive or negative which i know how to do but i am confused on how to figure out the final answer from that
• Sep 16th 2008, 04:59 PM
11rdc11
$2(x-3)-3(x+2)<5$

1) Distribute

$2x-6 -3x-6<6$

2) Combine like terms

$-x<18$

3) Divide by -1 and remember to change your sign

$x>-18$
• Sep 16th 2008, 05:04 PM
xian791
so there is only 1 answer? in the questions my teacher showed us there were mutiply answers like x^2(x-16)(x-3)<=0 and the answer was 3<=x<=16

and how you get <6 when it was <5?
• Sep 16th 2008, 05:09 PM
11rdc11
The amount of answers depend on the degree of the exponent. So in this case it was to the degree of 1 so you had 1 answer. Now $x^2$ is to the degree of 2 so you will have at most 2 solutions