How do you solve #-4/5(x-3)≤-12#?

1 Answer
EZ as pi
Jun 15, 2016

#x >= 18#

Explanation:

Treat inequalities in exactly the same way as an equation unless you are are multiplying or dividing by a negative number. In this case the inequality sign has to change around.
Also do not cross-multiply across an inequality.

Let's get rid of the annoying fraction outside the bracket by multiplying by #5/4#, leaving the minus sign there for now.

#color(red)(5/4) xx-4/5(x-3)<= color(red)(5/4) xx-12#

#=-(x-3) <=-15 " Multiplying out gives" #

#" "=-x +3 <=-15#

The problem now is the #-x#. The easiest is to move it to the right side to make it positive ;

#15 + 3 <=x#

#18 <= x# which can also be written as #x >= 18#

The other method would involve dividing by -1.
#-x <=-15 -3#
#-x <=-18 " divide by -1 "rArr" sign will change"#

#x >= 18#

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