How do you solve #9x - \frac { y} { 3} \leq 3y - 1#?

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Answer 1 · 2017-08-01T02:43:33

Two possible solutions.

Standard form for linear equations: #27x-10y=-3#.

Slope-intercept form for linear equations: #y>=27/10x+3/10#.

Solve:

#9x-y/3<=3y-1#

Multiply both sides by #3#.

#3(9x)-color(red)cancel(color(black)(3))(y/color(red)cancel(color(black)3))<=3(3y-1)#

Expand.

#27x-y<=9y-3#

Subtract #9y# from both sides.

#27x-y-9y<=-3#

Simplify.

#27x-10y=-3# #larr# Standard form for linear equation: #Ax+By=C#.

Solve for #y#.

Subtract #27x# from both sides.

#-10y<=-27x-3#

Divide both sides by #-10#. This will reverse the inequality.

#y>=(-27x)/(-10)-3/-10#

Simplify.

#y>=27/10x+3/10# #larr# Slope-intercept form for linear equation: #y=mx+b#.