How do you solve #abs(2x+7)>23#?

1 Answer
Oct 5, 2017

Answer:

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

#-23 > 2x + 7 > 23#

First, subtract #color(red)(7)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#-23 - color(red)(7) > 2x + 7 - color(red)(7) > 23 - color(red)(7)#

#-30 > 2x + 0 > 16#

#-30 > 2x > 16#

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

#-30/color(red)(2) > (2x)/color(red)(2) > 16/color(red)(2)#

#-15 > (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) > 8#

#-15 > x > 8#

Or

#x < -15# and #x > 8#

Or, in interval notation:

#(-oo, -15)# and #(8, +oo)#