SOLUTION: What's the answer to this |3n-1|>1

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Question 718384: What's the answer to this |3n-1|>1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Here's a procedure for these kinds of equations/inequalities:
  1. Isolate the absolute value.
  2. Rewrite the absolute value equation/inequality as two separate equations/inequalities:
    • Copy the equation/inequality from step 1 but omit the absolute value bar's.
    • There's three parts to the second equation/inequality:
      • Write the expression inside the absolute value (without the bars!).
      • For equations, just write an "=". For inequalities, reverse the inequality. (Change "<" to ">" and ">" ot "<".)
      • Write the negative of the other side of the equation/inequality.
  3. For equations or for absolute value's that are "greater than" something, write "or" between the two equations/inequalities from step 2. For absolute value's that are "less than" something, write "and" between the two equations/inequalities from step 2.
  4. At this point you should have either a pair of equations or a compound inequality. There should be no absolute values left. Solve these equations/inequalities.
  5. Graph the solution set on a number line if requested.
Let's see this in action:
abs%283n-1%29+%3E+1
1. Isolate the absolute value.
The absolute value is already all by itself on the left side.
2. Rewrite as two inequalities:
2a. Copy without absolute value bars:
3n-1+%3E+1
2b1. Rewrite the absolute value without the bars:
3n-1
2b2. Reverse the inequality:
3n-1 <
2b3. Write the negative of the other side. The negative of 1 is -1:
3n-1+%3C+-1
3. Write "or" or "and" between the two inequalities. abs%283n-1%29+%3E+1 says that the absolute value is greater than 1 so we write "or":
3n-1+%3E+1 or 3n-1+%3C+-1
4. Solve.
Adding to to both sides of both inequalities:
3n+%3E+2 or 3n+%3C+0
Divide both sides of both inequalities by 3:
n+%3E+2%2F3 or n+%3C+0
5. Graph, if requested.
To graph an "or" compound inequality you simply put the graph of each individual inequality on the same number line. The graph of n+%3E+2%2F3 would be an open circle at 2/3 with some shading going to the right from there (where the larger numbers are) with a ">" at the end of the shading to indicate "and so on forever in this direction". The graph of n+%3C+0 would be an open circle at 0 with some shading going to the left from there (where the smaller numbers are) with a "<" at the end of the shading to indicate "and so on forever in this direction". Just put both of these on the same number line. (Unfortunately Algebra.com's graphing software does not do graphs of inequalities on a number line.)