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Solve for [tex]\( x \)[/tex]:

[tex]\[ |x + 5| = -6 \][/tex]

Sagot :

GinnyAnswer
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.
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