To determine the number of solutions for the equation [tex]\( |x+7| = -4 \)[/tex], let's consider the properties of the absolute value function.
1. Understanding the absolute value: The absolute value of a number is always non-negative. That means [tex]\( |x+7| \geq 0 \)[/tex] for any real number [tex]\( x \)[/tex].
2. Inspecting the equation: The equation given is [tex]\( |x+7| = -4 \)[/tex].
3. Analyzing the right-hand side: The right-hand side of the equation is -4, which is a negative number.
4. Implication of the equation: Since the absolute value function always yields a non-negative result, it is impossible for [tex]\( |x+7| \)[/tex] to equal -4, as there is no real number [tex]\( x \)[/tex] that can satisfy this condition.
Therefore, there are no solutions for the equation [tex]\( |x+7| = -4 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{0} \][/tex]
Hence, the number of solutions is A) Zero.
