How do you solve #abs(11+4x)<23#?

Question

1460 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-08T23:50:26

The solution is the range for x: #-17/2 < x < 3#

Because this is an inequality with an absolute value function in it you must solve for both + and - 23 as follows:

#-23 < 11 + 4x < 23#

You must solve the series of inequalities while keeping all the inequalities balanced:

#-23 - 11 < 11 + 4x - 11 < 23 - 11#

#-34 < 0 + 4x < 12#

#-34 < 4x < 12#

#-34/4 < (4x)/4 < 12/4#

#(2/2)((-17)/2 < x < 3#

#-17/2 < x < 3#