∣x−2∣≤−2 solve the inequality.Dont spam otherwise you will be reported.
Answers
Given : |x - 2| ≤ -2
To find : Solve the inequality for x
Solution :
We have,
=> |x - 2| ≤ -2
=> x - 2 ≤ ± ( -2 )
So there arises two cases,
Case - I :
=> x - 2 ≤ - ( -2 )
=> x - 2 ≤ 2
=> x ≤ 2+2
=> x ≤ 4
Case - II :
=> x - 2 ≤ -2
=> x ≤ -2 + 2
=> x ≤ 0
Therefore critical points are, 4 and 0. These two points will divide the number line into three intervals.
- ( -∞ , 0 )
- ( 0 , 4 )
- ( 4, ∞ )
Now, to find the values of x satisfying the given inequality, we will substitute values from each interval and check whether the interval is a solution set or not.
For interval ( - ∞ , 0 ) => Substitute value - 1
=> | x - 2 | ≤ -2
=> | -1 - 2 | ≤ -2
=> | -3 | ≤ -2
=> 3 ≤ -2
This is not true, so the interval ( -∞, 0) is not a solution set.
For interval ( 0 , 4 ) => Substitute value 1
=> | x - 2 | ≤ -2
=> | 1 - 2 | ≤ -2
=> | - 1 | ≤ -2
=> 1 ≤ -2
This is also not true, so the interval ( 0, 4 ) is not a solution set.
For interval ( 4 , ∞ ) => Substitute value 5
=> | x - 2 | ≤ -2
=> | 5 - 2 | ≤ -2
=> | 3 | ≤ -2
=> 3 ≤ -2
Again this is not true, so the interval ( 4, ∞ ) is also not a solution set.
Therefore, there is no such real value of x which satisfies the given inequality.
No solution