How do you solve #14- 4k < 38#?

First, subtract #color(red)(14)# from each side of the inequality to isolate the #k# term while keeping the equation balanced:

#14 - color(red)(14) - 4k < 38 - color(red)(14)#

#0 - 4k < 24#

#-4k < 24#

Now, divide each side of the inequality by #color(blue)(-4)# to solve for #k# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#(-4k)/color(blue)(-4) color(red)(>) 24/color(blue)(-4)#

#(color(red)(cancel(color(black)(-4)))k)/cancel(color(blue)(-4)) color(red)(>) -6#

#k color(red)(>) -6#

We can treat this inequality like it's an equation. If our problem was instead #14-4k=38#, we would subtract #14# from both sides. We would do the same here to get:

#-4k<24#

Now, we divide both sides by #-4#, and here's the catch: Since we're dividing the inequality by a negative number, the direction of the sign will flip. This would even hold true of we're multiplying. We get:

#k> -6#

#14-4k<38#

Start by subtracting #14# on both sides

#14 - 4k - 14 < 38 - 14#

#-4k < 24#

Divide both sides by #-4#
#(cancel(-4)k)/cancel(-4) < 24/(-4)#

#k > -6#

Note:

When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the sign as well. If it was #<#, it will be #>#. Got it?