How do you solve and graph #–2x < 14 #?

You can solve this inequality by isolating #x# on one side, something that can be done by dividing both sides of the equation first by #2#

#(-color(red)(cancel(color(black)(2)))x)/color(red)(cancel(color(black)(2))) < 14/2#

#-x < 7#

Now take a look at how the inequality looks like. You need minus #x# to be smaller than #7#. It's obvious that any positive value of #x# will satisfy this equation, since

#-x <0" ",AAx>0#

This is true for some negative values of #x# as well, more precisely for values of #x# that are bigger than #x = -7#. For values of #x# that are smaller than #-7#, you have

#-(-8) < 7 implies 8 color(red)(cancel(color(black)(<))) 7#

This means that any value of #x# that is greater than #7# will satisfy this inequality.

#x > color(green)(-7)#

This is why when you divide both sides ofan inequality by #-1#, like you would to isolate #x#, you must flip the inequality sign.

#(color(red)(cancel(color(black)(-1)))x)/color(red)(cancel(color(black)(-1))) color(green)(>) 7/(-1)#

#x > -7#

To graph the solution set for this inequality, draw a dotted vertical line parralel to the #y#-axis that goes through #x = -7#. Since you want all values of #x# that are greater than #-7#, you must shade the area to the right of the dotted line.

The fact that the line is dotted indicates that #x=-7# is not part of the solution set.

graph{x> -7 [-10, 10, -5, 5]}