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how do I translate the absolute value of three times a number, n, is greater than 15?

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2 Answers

|3n| > 15
To solve an absolute value inequality, you write two separate equations. The first keeps the expression in the absolute value bars positive with the same inequality, while the other negates the expression in the absolute value bars with the opposite inequality. In this case, the two equations are:
3n > 15          -3n < 15
Now solve for n in each:
3n > 15          -3n < 15
n > 5              n < -5
If we set up a number line, we get the intervals for which the original inequality is true:
              -5                        5
So the answer is n > 5, n < -5, or in interval notation (-∞, -5) V (5, ∞)
we know that for two positive numbers x and y,  lxl>y means that x<-y or x>y. Therefore,
3n<-15   or  3n>15
Dividing both sides of the inequalities by 3 we have:
n<-5   or n>5