How do you solve #−5x + 8 <= x − 4#?

1 Answer
Aug 15, 2015

Answer:

#x >=2#

Explanation:

Isolate #x# on one side of the inequality, first by adding #-x# to both sides to get

#-5x + 8 - x <= color(red)(cancel(color(black)(x))) - color(red)(cancel(color(black)(x))) - 4#

#-6x + 8 <= -4#

Next, add #-8# to both sides of the inequality

#-6x + color(red)(cancel(color(black)(8))) - color(red)(cancel(color(black)(8))) <= -4 - 8#

#-6x <= -12#

FInally, divide both sides by #-6#, but do not forget that you need to change the sign of the inequality when you're multiplying or dividing by a negative number

#(color(red)(cancel(color(black)(-6)))x)/color(red)(cancel(color(black)(-6))) color(red)(>=) ((-12))/((-6))#

#x >= color(green)(2)#

So, for any value of #x# that is greater to or equal than #2#, your original inequality will be true.