How do you solve #36\leq 12( \frac { 1} { 3} z + \frac { 2} { 3} )#?

1 Answer
smendyka
Apr 3, 2017

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

#36 <= color(red)(12)(1/3z + 2/3)#

#36 <= (color(red)(12) xx 1/3z) + (color(red)(12) xx 2/3)#

#36 <= 4z + 8#

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

#36 - color(red)(8) <= 4z + 8 - color(red)(8)#

#28 <= 4z + 0#

#28 <= 4z#

Now, divide each side of the inequality by #color(red)(4)# to solve for #z# while keeping the inequality balanced:

#28/color(red)(4) <= (4z)/color(red)(4)#

#7 <= (color(red)(cancel(color(black)(4)))z)/cancel(color(red)(4))#

#7 <= z#

To put this solution in terms of #z# we can reverse or "flip" the inequality:

#z >= 7#

Related questions
Impact of this question
334 views around the world
You can reuse this answer
Creative Commons License