How do you solve a linear inequality #3x + 2y < 6#?

1 Answer
Jul 20, 2018

#" "#
#color(red)(y<(6-3x)/2#

Explanation:

#" "#
We are given the inequality: #color(blue)(3x+2y<6#

#rArr 3x+2y<6#

Subtract #color(red)(3x# from both sides of the inequality.

#rArr 3x+2y -3x< 6-3x#

#rArr cancel(3x)+2y -cancel(3x)< 6-3x#

#rArr 2y< 6-3x#

Divide both sides of the inequality by #color(red)(2#

#rArr (2y)/2< (6-3x)/2#

#rArr (cancel 2y)/cancel 2< (6-3x)/2#

#rArr y<(6-3x)/2#

Hence, our final solution is given by:

#color(blue)(y<(6-3x)/2#

We can also graph this solution as given below:

Note that the dotted line in the graph indicates value that is NOT a part of the final solution.

enter image source here

Hope this helps.