How do you solve the x in #-ax+2b>8#?

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Answer 1 · 2017-01-02T23:18:31

See full solution process details below:

The first step is to subtract #color(blue)(2b)# from each side of the inequality to isolate the #x# term:

#-ax + 2b - color(blue)(2b) > 8 - color(blue)(2b)#

#-ax + 0 > 8 - color(blue)(2b)#

#-ax > 8 - color(blue)(2b)#

Now we can divide each side of the inequality by #color(red)(-a)# to solve for #x# and keep the inequality balanced.

However, because we are multiplying or dividing by a negative term we need to also reverse the inequality:

#(-ax)/color(red)(-a) color(green)(<) (8 - color(blue)(2b))/color(red)(-a)#

#(color(red)(cancel(color(black)(-a)))x)/cancel(color(red)(-a)) color(green)(<) (8 - color(blue)(2b))/color(red)(-a)#

#x < (8 - 2b)/-a#