Given:
The inequality is
[tex]5(3-x)<-2x+6[/tex]
To find:
The inequality that solution describes all the solutions to the given inequality.
Solution:
We have,
[tex]5(3-x)<-2x+6[/tex]
Using distributive property, we get
[tex]5(3)+5(-x)<-2x+6[/tex]
[tex]15-5x<-2x+6[/tex]
[tex]15-6<-2x+5x[/tex]
[tex]9<3x[/tex]
Divide both sides by 3.
[tex]\dfrac{9}{3}<x[/tex]
[tex]3<x[/tex]
It can be written as
[tex]x>3[/tex]
Therefore, the value of x is greater than 3. So, the required inequality is either [tex]x>3[/tex] or [tex]3<x[/tex].
