Answer :
Let's solve the equation step-by-step:
[tex]\[ e|x+5| = -6 \][/tex]
### Step 1: Analyze the equation
An important observation is that the absolute value function [tex]\( |x+5| \)[/tex] always outputs a non-negative value (i.e., it is always greater than or equal to zero). Also, the constant [tex]\( e \)[/tex] (Euler's number) is a positive number (approximately 2.71828).
When we multiply [tex]\( e \)[/tex] (which is positive) with [tex]\( |x+5| \)[/tex] (which is non-negative), the result will always be non-negative.
### Step 2: Observe the right side
The right side of the equation is [tex]\(-6\)[/tex], which is negative.
### Step 3: Compare both sides
We now have the expression:
[tex]\[ \text{non-negative value} = -6 \][/tex]
Since a non-negative value can never be equal to a negative value, there is a fundamental contradiction here.
### Conclusion
There are no real values for [tex]\( x \)[/tex] that can satisfy the equation:
[tex]\[ e|x+5| = -6 \][/tex]
So, the equation has no solutions.
[tex]\[ e|x+5| = -6 \][/tex]
### Step 1: Analyze the equation
An important observation is that the absolute value function [tex]\( |x+5| \)[/tex] always outputs a non-negative value (i.e., it is always greater than or equal to zero). Also, the constant [tex]\( e \)[/tex] (Euler's number) is a positive number (approximately 2.71828).
When we multiply [tex]\( e \)[/tex] (which is positive) with [tex]\( |x+5| \)[/tex] (which is non-negative), the result will always be non-negative.
### Step 2: Observe the right side
The right side of the equation is [tex]\(-6\)[/tex], which is negative.
### Step 3: Compare both sides
We now have the expression:
[tex]\[ \text{non-negative value} = -6 \][/tex]
Since a non-negative value can never be equal to a negative value, there is a fundamental contradiction here.
### Conclusion
There are no real values for [tex]\( x \)[/tex] that can satisfy the equation:
[tex]\[ e|x+5| = -6 \][/tex]
So, the equation has no solutions.
