How do you solve #2\leq - 4+ \frac { 8x } { 9}#?

2 Answers
MysticSmile
Sep 20, 2017

#xge27/4# or #6 3/4# or #6.75#

Explanation:

First, we switch sides to #-4+(8x)/9ge2# and add #4# to both sides.

#-4+(8x)/9color(blue)+color(blue)4ge2color(blue)+color(blue)4#.

Simplify it to be #(8x)/9ge6#. Multiply both sides by #9#.
#(color(blue)9color(blue)*8x)/9ge6color(blue)*color(blue)9# which is #8xge54#.

Next we divide both sides by 8.

#(8x)/color(blue)8ge54/color(blue)8#.

SImplify it to be #xge27/4# or #6 3/4# or #6.75#.

Jim G.
Sep 20, 2017

#x>=27/4#

Explanation:

#"add 4 to both sides of the inequality"#

#2+4<=cancel(-4)cancel(+4)+(8x)/9#

#rArr6<=(8x)/9#

#"multiply both sides by 9"#

#(9xx6)<=cancel(9)xx(8x)/cancel(9)#

#rArr54<=8x#

#"divide both sides by 8"#

#54/8<=x#

#27/4<=xrArrx>=27/4#

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