How do you solve and graph #4x-3<2x#?

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Answer 1 · 2015-08-13T11:57:49

#x < 3/2#

You can solve this inequality by isolating #x# on one side.

This can be done in three steps. First, add #3# to both sides of the inequality to get

#4x - color(red)(cancel(color(black)(3))) + color(red)(cancel(color(black)(3))) < 2x + 3#

#4x < 2x + 3#

Now add #-2x# to both sides of the inequality

#4x - 2x < color(red)(cancel(color(black)(2x))) - color(red)(cancel(color(black)(2x))) + 3#

#2x < 3#

Finally, divide both sides of the inequality by #2# to isolate #x#

#(color(red)(cancel(color(black)(2)))x)/color(red)(cancel(color(black)(2))) < 3/2#

#x < color(green)(3/2)#

To graph the solution set for this inequality, draw a dotted vertical line parallel to the #y#-axis that goes through #x=3/2#.

Since you want all the #x# values that are smaller than #3/2#, shade the region to the left of #x=3/2#.

The dotted line signifies that #x=3/2# is not a part of the solution set.

graph{x<3/2 [-10, 10, -5, 5]}