How do you solve #8-z/3>=11#?

2 Answers
Nam D.
Mar 7, 2018

#z<=-9#

Explanation:

We are given:

#8-z/3>=11#

Now, we can solve it with the following steps.

#-z/3>=11-8#

#-z/3>=3#

Multiplying by #3# on both sides, we get

#-z>=9#

We now need #z# instead of #-z#, so we divide by #-1#.

When dividing by a negative number, we must inverse the inequality sign.

#z<=-9#

smendyka
Mar 7, 2018

See a solution process below:

Explanation:

First, subtract #color(red)(8)# from each side of the inequality to isolate the #z# term while keeping the inequality balanced:

#8 - color(red)(8) - z/3 >= 11 - color(red)(8)#

#0 - z/3 >= 3#

#-z/3 >= 3#

Now, multiply each side of the inequality by #color(blue)(-3)# to solve for #z# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#color(blue)(-3) xx -z/3 color(red)(<=) color(blue)(-3) xx 3#

#color(blue)(-3) xx z/-3 color(red)(<=) -9#

#cancel(color(blue)(-3)) xx z/color(blue)(cancel(color(black)(-3))) color(red)(<=) -9#

#z <= -9#

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