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Describe the steps you would use to solve the inequality. $$11-2 n>-5$$
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Video Transcript
11 minus two n. All right, eyes greater than negative five. And we're describing the steps we would use to solve this. We're not actually solving it, but all right, so to solve this and get Anil by itself, I would subtract 11 from all sides and divide all sides. I negative, too. And gotta remember to flip the sign. Thanks. Inequality. Sign What flipped the inequality when dividing I a negative, which we are doing here.
Question
Gauthmathier9045
Grade 8 · 2022-01-07
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What is the solution to the inequality
What is the solution to the inequality |2n+5|>1 �� - Gauthmath ？
-3>n>-2
2<n<3
n<-33 or
n>-2
n<2 or
n>3
Ali
University of Chicago
Master's degree
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(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
//www.wolframalpha.com/input/?i=%7C2n%2B5%7C+%3E+1
Absolute value inequalities
We think you wrote:
This solution deals with absolute value inequalities.
Step by Step Solution
Absolute Value Inequality entered :
|2n-5|<1
Step by step solution :
Step 1 :
Rearrange this Absolute Value Inequality
Absolute value inequalitiy entered
|2n-5| < 1
Step 2 :
Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |2n-5|For the Negative case we'll use -(2n-5)
For the Positive case we'll use (2n-5)
Step 3 :
Solve the Negative Case
-(2n-5) < 1
Multiply
-2n+5 < 1
Rearrange
and Add up
-2n < -4
Divide both sides by 2
-n < -2
Multiply both sides by (-1)
Remember to flip the inequality sign
n > 2
Which is the solution
for the Negative Case
Step 4 :
Solve the Positive Case
(2n-5) < 1
Rearrange and Add up
2n < 6
Divide both sides by 2
n < 3
Which is the solution for the Positive Case
Step 5 :
Wrap up the solution
2 < n < 3
Solution in Interval Notation
(2,3)
Solution on the Number Line
One solution was found :
2 < n < 3