What is the solution to the inequality |2n+5|>1?
A. –3 > n > –2
B. 2 < n < 3
C. n < –3 or n > –2
D. n < 2 or n > 3
I put A! :) Thank you again.
(2n+5) > 1
2n > -4
n > -2
-(2n+5) > 1
2n+5 < -1
2n < -6
n < -3
Think of the shape of |x| -- it is a V-shape. So, if |x| > n, it will be where the graph is above the line y=n. That means there will be two intervals, not one. See
http://www.wolframalpha.com/input/?i=%7C2n%2B5%7C+%3E+1
To solve the inequality |2n+5| > 1, we need to consider two possibilities: 2n+5 is either positive or negative.
1. When 2n+5 is positive:
If 2n+5 > 1, we can solve this inequality as follows:
2n > 1 - 5 (subtracting 5 from both sides)
2n > -4
Now, divide both sides by 2 to solve for n:
n > -2
2. When 2n+5 is negative:
If -(2n+5) > 1, we can solve this inequality as follows:
-2n - 5 > 1 (multiplying both sides by -1 to change the direction of the inequality)
-2n > 1 + 5 (adding 5 to both sides)
-2n > 6
Now, divide both sides by -2 (since we want to isolate n):
n < -3
Combining both possibilities, we find that either n > -2 or n < -3. Therefore, the correct answer is option C: n < –3 or n > –2.
To solve the inequality |2n+5|>1, we need to consider two cases.
Case 1: (2n+5) > 1.
Solving this inequality gives us 2n > -4, which simplifies to n > -2.
Case 2: -(2n+5) > 1.
By multiplying both sides by -1, we get 2n+5 < -1. Solving this inequality gives us 2n < -6, which simplifies to n < -3.
Therefore, the solution to the inequality |2n+5|>1 is n < -3 or n > -2.
So, the correct answer is C: n < -3 or n > -2.