How do you solve #-2z - 3.8> - 30.6+ 2z#?

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Answer 1 · 2017-08-27T14:09:42

See a solution process below:

First, add #color(red)(2z)# and #color(blue)(30.6)# to each side of the inequality to isolate the #z# term while keeping the inequality balanced:

#-2z - 3.8 + color(red)(2z) + color(blue)(30.6) > -30.6 + 2z + color(red)(2z) + color(blue)(30.6)#

#-2z + color(red)(2z) - 3.8 + color(blue)(30.6) > -30.6 + color(blue)(30.6) + 2z + color(red)(2z)#

#0 + 26.8 > 0 + (2 + color(red)(2))z#

#26.8 > 4z#

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

#26.8/color(red)(4) > (4z)/color(red)(4)#

#6.7 > (color(red)(cancel(color(black)(4)))z)/cancel(color(red)(4))#

#6.7 > z#

We can reverse or "flip" the entire inequality to state the solution in terms of #z#:

#z < 6.7#