How do you solve #|(3x + 4 )/ 6| = |-4|#?

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Answer 1 · 2017-04-24T02:14:15

#"For"# #|(3x+4)/6|=|-4|#

#x=20/3,-28/3#

For absolute value you are going to solve for positive and negative.
Like this.

#|(3x+4)/6|=|-4|#

So we are solving

#|(3x+4)/6|=4# #color(red)"AND"# #|(3x+4)/6|=-4#

#color(red)(|(3x+4)/6|=4)#

Multiply both sides by six to remove denominator
#(3x+4)/cancel6=4*6#

#3x+4=24#

Subtract 4 from both sides
#3xcancel(+4)=24-4#
#3x=20#

Divide by 3 so that we have "x" alone
#(cancel3x)/cancel3=20/3#

#x=20/3#

Now, #color(red)(|(3x+4)/6|=-4)#

This is the same process so I'll go through it a little quicker.

#|(3x+4)/cancel6|=-4*6#

#3x+4=-24#

#3xcancel(+4)=-24-4#

#3x=-28#

#x=-28/3#