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How many solutions does the equation [tex]|x+7|=-4[/tex] have?

A) Zero
B) Exactly one
C) Exactly two
D) More than two

Sagot :

GinnyAnsweridn
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.
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