How do you solve #7\leq 3y + 13\leq 13#?

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Answer 1 · 2017-02-22T12:47:18

See the entire solution process below"

When solving a system of inequalities you must perform all actions against each segment of the system to keep all the inequalities balanced.

First, subtract #color(red)(13)# from the system:

#7 - color(red)(13) <= 3y + 13 - color(red)(13) <= 13 - color(red)(13)#

#-6 <= 3y + 0 <= 0#

#-6 <= 3y <= 0#

Now, divide the system by #color(red)(3)#

#-6/color(red)(3) <= (3y)/color(red)(3) <= 0/color(red)(3)#

#-2 <= (color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) <= 0#

#-2 <= y <= 0#