Answer:
C: n < –3 or n > –2
Step-by-step explanation:
We are given
[tex]|2n+5| > 1[/tex]
and asked to find the solution set for n
The absolute rule says that
if |u| > a with a > o then
u < - a or u > a
Here u represents the left side of the inequality
Substituting for u = |2n + 5| we get
2n + 5 < - 1
or
2n + 5 > 1
2n + 5 < - 1
==> 2n < -1 - 5 (subtract 5 from both sides)
==> 2n < - 6 (simplify right side)
==> n < -3 (dividing both sides by 2)
2n + 5 > 1
==> 2n > -5 + 1 (subtract 5 from both sides)
==> 2n > -4 (simplify right side)
==> n > -2 (dividing both sides by 2)
We can rewrite this as
n < -3 or n > - 2
which is choice C
Answer:
C) n < -3 or n > -2
Step-by-step explanation:
Given absolute value inequality:
[tex]|2n+5| > 1[/tex]
To solve an inequality containing an absolute value, we create two separate cases by considering both the positive and negative contents of the absolute value:
[tex]\textsf{Case 1:}\quad (2n+5) > 1[/tex]
[tex]\textsf{Case 2:}\quad -(2n+5) > 1[/tex]
Solve each case for n, remembering that when we divide (or multiply) both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign:
[tex]\boxed{\begin{array}{c|c}\underline{\sf Case\;1}&\underline{\sf Case\;2}\\\\\begin{aligned}(2n+5)& > 1\\\\2n+5& > 1\\\\2n+5-5& > 1-5\quad\\\\2n& > -4\\\\\dfrac{2n}{2}& > \dfrac{-4}{2}\\\\n& > -2\end{aligned}&\begin{aligned}-(2n+5)& > 1\\\\-2n-5& > 1\\\\\quad-2n-5+5& > 1+5\\\\-2n& > 6\\\\\dfrac{-2n}{-2}& < \dfrac{6}{-2}\\\\n& < -3\end{aligned}\end{array}}[/tex]
As the two intervals do not overlap, the solution is:
[tex]\Large\boxed{\boxed{n < -3\;\;\textsf{or}\;\;n > -2}}[/tex]
Learn more about absolute value inequalities here:
https://brainly.com/question/31017380
