How do you solve and write the following in interval notation: #-6x + 2< -3x -12#?

1 Answer
Apr 27, 2017

Answer:

See the entire solution process below:

Explanation:

First, add #color(red)(6x)# and #color(blue)(12)# to each side of the inequality to isolate the #x# term while keeping the equation balanced:

#color(red)(6x) - 6x + 2 + color(blue)(12) < color(red)(6x) - 3x - 12 + color(blue)(12)#

#0 + 14 < (color(red)(6) - 3)x - 0#

#14 < 3x#

Now, divide each side of the equation by #color(red)(3)# to solve for #x# while keeping the equation balanced:

#14/color(red)(3) < (3x)/color(red)(3)#

#14/3 < (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))#

#14/3 < x#

Or, in interval notation:

#(-oo, 14/3)#