Inequality

harpazo

Pure Mathematics
Banned
Mar 20, 2018
5,788
361
83
NYC
x^2 - 3x - 18 > 0

( x - 6 ) ( x + 3 ) > 0

x - 6 > 0

x > 6

or

x + 3 > 0

x > -3

This does not seem right.
 

TheJason

Administrator
Staff member
Administrator
Moderator
Jan 25, 2018
2,508
545
113
jasonyankee.info
Looks correct to me.
 
Last edited:

MarkFL

La Villa Strangiato
Staff member
Administrator
Moderator
Math Helper
Jan 25, 2018
3,496
4,276
113
St. Augustine
Let's stop at this point in your work:

\(\displaystyle (x-6)(x+3)>0\)

We know the original expression, the quadratic, has a graph that's a parabola opening upwards, so the positive portion of the graph will be to either side of the two roots, thus the solution set is:

\(\displaystyle (-\infty,-3)\,\cup\,(6,\infty)\)
 
  • Like
Reactions: anemone and harpazo

harpazo

Pure Mathematics
Banned
Mar 20, 2018
5,788
361
83
NYC