How do you solve #-3/8(16x - 8) >4#?

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Answer 1 · 2016-09-02T16:12:28

#x <-1/6#

Treat it the same as an equation, unless you multiply or divide by a negative, in which case the sign in the middle changes around.

I have used two methods. I thought the first would be quicker and easier - it wasn't.!!

Second method is much better.

Method 1 Isolate the bracket first.

#-3/8(16x - 8) >4 larr " multiply by "-8/3#

#color(red)(-8/3xx)-3/8(16x - 8) < 4 color(red)(xx-8/3) " note" > to<#

#16x-8 <-32/3#

#16x < -32/3 +8#

#16x < -8/3#

#x < -cancel8/(3xxcancel16^2)#

#x <-1/6#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Method 2 Remove the brackets with distributive law.

#-3/8(16x - 8) >4#

#-6x +3 >4#

#3-4 >6x#

#-1 > 6x#

#-1/6 >x#

This is the same as #x<-1/6#