How do you solve and graph #3y+6<=2y#?

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Answer 1 · 2017-12-16T13:49:44

See a solution process below:

Subtract #color(red)(6)# and #color(blue)(2y)# from each side of the inequality to solve for #y# while keeping the inequality balanced:

#3y - color(blue)(2y) + 6 - color(red)(6) <= 2y - color(blue)(2y) - color(red)(6)#

#(3 - color(blue)(2))y + 0 <= 0 - 6#

#1y <= -6#

#y <= -6#

To graph this we will draw a horizontal line at #-6# on the veritical axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade below the line because the inequality operator also contains a "less than" clause:

graph{y <= -6 [-30, 30, -15, 15]}