Solve absolute value equation or indicate the equation has no

quiquenobi2v6

quiquenobi2v6

Answered question

2021-12-07

Solve absolute value equation or indicate the equation has no solution.
|x + 1 | + 5 = 3

Answer & Explanation

redhotdevil13l3

redhotdevil13l3

Beginner2021-12-08Added 30 answers

Step 1
Consider the given equation |x+1|+5=3
Step 2
Simplify as
|x+1|=3−5
|x+1|=-2
Use the property of absolute value
|xa|={xax>a(xa)x<a} where a>0 then
x+1=-2 for x>-1 and -(x+1)=-2 for x<-1
First simplify as
x+1=-2
x=-2-1
x=-3
Step 3
But it is not true for x>-1.
Now simplify -(x+1)=−2 for x<-1 as
-x+1=-2
-x=-2-1
-x=-3
x=3
But it is not true for x<−1
Hence the given equation does not have any solution.

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