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Solve [tex]\( |x+6| = -8 \)[/tex]

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GinnyAnsweridn
To solve the equation [tex]\( |x + 6| = -8 \)[/tex], let's carefully analyze the properties of absolute value expressions.

1. Understanding Absolute Value:
The absolute value of a number, denoted by [tex]\( |a| \)[/tex], is defined as the distance of [tex]\( a \)[/tex] from zero on the number line. It always results in a non-negative number, meaning [tex]\( |a| \geq 0 \)[/tex] for any real number [tex]\( a \)[/tex].

2. Equation Analysis:
Given the equation [tex]\( |x + 6| = -8 \)[/tex]:
- We need to recognize that an absolute value expression [tex]\( |x + 6| \)[/tex] can never be negative.
- Therefore, the equation [tex]\( |x + 6| = -8 \)[/tex] is asking us to find a value of [tex]\( x \)[/tex] such that the non-negative absolute value of [tex]\( x + 6 \)[/tex] is equal to [tex]\(-8\)[/tex].

3. Checking for Solutions:
- Since the absolute value cannot be negative, the equation [tex]\( |x + 6| = -8 \)[/tex] does not make any sense in the set of real numbers.
- There are no real numbers [tex]\( x \)[/tex] such that the absolute value of [tex]\( x + 6 \)[/tex] equals a negative number.

4. Conclusion:
Given the properties of absolute values, it is clear that there is no solution to the equation [tex]\( |x + 6| = -8 \)[/tex].

Hence, the equation [tex]\( |x + 6| = -8 \)[/tex] has no solution.
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