How do you solve #2(2m-5)-6> -36#?

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Answer 1 · 2018-03-14T18:29:17

See a solution process below:

First, add #color(red)(6)# to each side of the inequality to isolate the term with the parenthesis while keeping the inequality balanced:

#2(2m - 5) - 6 + color(red)(6) > -36 + color(red)(6)#

#2(2m - 5) - 0 > -30#

#2(2m - 5) > -30#

Next, divide each side of the inequality by #color(red)(2)# to eliminate the need for parenthesis while keeping the inequality balanced:

#(2(2m - 5))/color(red)(2) > -30/color(red)(2)#

#(color(red)(cancel(color(black)(2)))(2m - 5))/cancel(color(red)(2)) > -15#

#2m - 5 > -15#

Then, add #color(red)(5)# to each side of the inequality to isolate the #m# term while keeping the inequality balanced:

#2m - 5 + color(red)(5) > -15 + color(red)(5)#

#2m - 0 > -10#

#2m > -10#

Now, divide each side of the inequality by #color(red)(2)# to solve for #m# while keeping the inequality balanced:

#(2m)/color(red)(2) > -10/color(red)(2)#

#(color(red)(cancel(color(black)(2)))m)/cancel(color(red)(2)) > -5#

#m > -5#