How do you solve #-\frac { x } { 6} + \frac { 22} { 6} \leq - \frac { 6x } { 3}#?

1 Answer
Jim G.
Oct 24, 2017

#x<=-2#

Explanation:

#"multiply ALL terms on both sides of the inequality by the"#
#color(blue)"lowest common multiple ""of 6 and 3"#

#"the lowest common multiple of 6 and 3 is "6#

#(cancel(6)xx-x/cancel(6))+(cancel(6)xx22/cancel(6)) <=cancel(6)^2xx-(6x)/cancel(3)^1)#

#rArr-x+22<=-12xlarrcolor(blue)" no fractions"#

#"add 12x to both sides"#

#-x+12x+22<=cancel(-12x)cancel(+12x)#

#rArr11x+22<=0#

#"subtract 22 from both sides"#

#11xcancel(+22)cancel(-22)<=0-22#

#rArr11x<=-22#

#"divide both sides by 11"#

#(cancel(11) x)/cancel(11)<=(-22)/11#

#rArrx<=-2" is the solution"#

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