How do you solve and graph #|2x + 1| – 3 >6#?

1 Answer
Aug 11, 2017

Answer:

See a solution process below:

Explanation:

First, add #color(red)(3)# to each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

#abs(2x + 1) - 3 + color(red)(3) > 6 + color(red)(3)#

#abs(2x + 1) - 0 > 9#

#abs(2x + 1) > 9#

The absolute value function takes any number and transforms it to its non-negative form. Therefore we need to solve the term within the absolute value function for both the negative and positive value it is equated to.

#-9 > 2x + 1 > 9#

Next, subtract #color(red)(1)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#-9 - color(red)(1) > 2x + 1 - color(red)(1) > 9 - color(red)(1)#

#-10 > 2x + 0 > 8#

#-10 > 2x > 8#

Now, divide each segment by ## while keeping the system balanced:color(red)(2)

#-10/color(red)(2) > (2x)/color(red)(2) > 8/color(red)(2)#

#-5 > (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) > 4#

#-5 > x > 4#

Or

#x < -5# and #x > 4#

Or, in interval notation:

#(-oo, -5)# and #(4, +oo)#