To solve the equation [tex]\( |x + 6| = -8 \)[/tex], we need to understand the properties of absolute values.
The absolute value function, denoted as [tex]\( |a| \)[/tex], represents the distance of [tex]\( a \)[/tex] from zero on the number line. By definition, absolute values are always non-negative because distance cannot be negative.
Given the equation [tex]\( |x + 6| = -8 \)[/tex], we can observe the following:
1. The expression [tex]\( |x + 6| \)[/tex] denotes the absolute value of [tex]\( x + 6 \)[/tex].
2. Absolute values cannot be negative numbers. Therefore, there is no value of [tex]\( x \)[/tex] that can satisfy the equation [tex]\( |x + 6| = -8 \)[/tex].
As a result, the equation [tex]\( |x + 6| = -8 \)[/tex] has no solution.
Thus, the correct answer is:
C. No solution
