How do you solve #\frac { 2} { 9} x - \frac { 20} { 27} > - 1#?

1 Answer
smendyka
Jun 2, 2017

See a solution process below:

Explanation:

First, add #color(red)(20/27)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#2/9x - 20/27 + color(red)(20/27) > -1 + color(red)(20/27)#

#2/9x - 0 > (27/27 xx -1) + color(red)(20/27)#

#2/9x > -27/27 + color(red)(20/27)#

#2/9x > -7/27#

Now, multiply each side of the inequality by #color(red)(9)/color(blue)(2)# to solve for #x# while keeping the inequality balanced:

#color(red)(9)/color(blue)(2) xx 2/9x > color(red)(9)/color(blue)(2) xx -7/27#

#cancel(color(red)(9))/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(2)))/color(red)(cancel(color(black)(9)))x > cancel(color(red)(9))/color(blue)(2) xx -7/(color(red)(cancel(color(black)(27)))3)#

#x > -7/6#

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