To solve the equation [tex]\( |x + 5| = -6 \)[/tex], we need to recall the properties of absolute values. The absolute value function, denoted by [tex]\( | \cdot | \)[/tex], always returns a non-negative result, meaning it is either zero or positive.
An absolute value equation [tex]\( |x| = y \)[/tex] has solutions if and only if [tex]\( y \geq 0 \)[/tex]. In simpler terms, the right-hand side of the equation must be zero or a positive number.
However, in the given equation [tex]\( |x + 5| = -6 \)[/tex], the right side is [tex]\(-6\)[/tex], which is a negative number. Since the absolute value of any real number cannot be negative, it is impossible for [tex]\( |x + 5| \)[/tex] to equal [tex]\(-6\)[/tex].
Therefore, the equation [tex]\( |x + 5| = -6 \)[/tex] has no solution.
Hence, the correct answer is:
C. No solution
