Answered

From simple queries to complex problems, IDNLearn.com provides reliable answers. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.

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

Sagot :

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.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.