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21 votes
21 votes
How do you solve the following:
−3+ |n-2 | >5

Please help!!!!

User Alcedo
by
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1 Answer

24 votes
24 votes

Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.

If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.

If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.

Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).

User Hum
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