How do you solve the inequality #-9 - e > 3e + 11#?

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Answer 1 · 2018-07-24T19:03:37

#e < -5#

#-9 - e > 3e + 11#

Add #color(blue)e# to both sides:
#-9 - e quadcolor(blue)(+quade) > 3e + 11 quadcolor(blue)(+quade)#

#-9 > 4e + 11#

Subtract #color(blue)11# from both sides:
#-9 quadcolor(blue)(-quad11) > 4e + 11 quadcolor(blue)(-quad11)#

#-20 > 4e#

Divide both sides by #color(blue)4#:
#(-20)/color(blue)4 > (4e)/color(blue)4#

#-5 > e#

Therefore,
#e < -5#

Here's a graph of it on a number line:
enter image source here

The open circle on #-5# means that #-5# is not a solution (but anything else less than it).

Hope this helps!