apaulus4907
Answered

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

A. [tex]\( x = -2 \)[/tex] and [tex]\( x = -14 \)[/tex]

B. [tex]\( x = -2 \)[/tex] and [tex]\( x = 14 \)[/tex]

C. No solution

D. [tex]\( x = 2 \)[/tex] and [tex]\( x = -14 \)[/tex]

Sagot :

GinnyAnswer
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
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