How do you solve and graph #(3x - 5) / 2 < 2x + 2#?

1 Answer
Stefan V.
Aug 28, 2015

#x> -9#

Explanation:

Your goal here is to isolate #x# on one side of the inequality. Start by multiplying the right-hand side of the inequality by #1= 2/2#

#(3x-5)/2 < (2x+2) * 2/2#

This is equivalent to

#3x - 5 < 2(2x+2)#

#3x-5 < 4x + 4#

Now move #-5# and #4x# on the other sides of the inequality - don't forget to change their signs when you do that!

#3x - 4x < 4+ 5#

#-x < 9#

#x > -9#

This means that your inequality will be satisfied by any value of #x# that is bigger than #-9#. The solution set will be #x in (-9, + oo)#.

You can graph this by drawing a dashed vertical line at #x=-9#. Since you need the values of #x# that are bigger than #-9#, shade the area to the right of the dashed vertical line.

graph{x > -9 [-18.02, 18.03, -9.01, 9.01]}

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