How do you solve #|3- 5n | > 8#?

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Answer 1 · 2017-09-22T15:17:39

#n > 11/15#, #n < -1#

To solve inequalities involving absolute values we have to solve for the possibility of the expression in the bars being both positive and negative.

First just remove bars:

#3 - 5n > 8#

Subtract 3 from both sides:

#-5n > 5#

Divide both sides by #-5#(and reverse the inequality sign)

#n < -1#

Now we have to solve for:

#|-(3 - 5n)| > 8#

Remove bars:

#-(3 - 5n) > 8#

remove bracket:

#-3 + 15n > 8#

Add 3 to both sides:

#15n > 11#

Divide by 11:

#n > 11/15#

These results can be written:

#n > 11/15#, #n < -1#

or as a union of intervals:

#(-oo , -1 ) uuu (11/15 , +oo )#

See graph: