How do you solve #|-2x + 8| <20#?

1 Answer
Apr 17, 2018

Answer:

#x > -6#, #x < 14#

Explanation:

#| -2x+8 | < 20#

We can have solutions, where the terms inside the absolute value is #-(-2x+8)# or #(-2x+8)#. So we need to solve for both of these

#* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *#

#-( -2x+8 ) < 20#

#-2x + 8 > -20#

note that the sign changed direction. This occurs anytime we multiply or divide by a negative number

# -2x > -20 - 8#

# -x > -28/2#

# x < 14 #

#* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *#

#-2x + 8 < 20#

#-2x < 20-8#

#-2x < 12#

#-x < 6#

#x > -6#

To check our work, let's graph the original function and see if it is less than #14# and greater than #-6#

Yep, it is, so we were right!