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Solve [tex]|x+4|=-6[/tex].

A. No solution
B. [tex]x=-2[/tex] and [tex]x=10[/tex]
C. [tex]x=-2[/tex] and [tex]x=-10[/tex]
D. [tex]x=2[/tex] and [tex]x=-10[/tex]


Sagot :

To solve the equation [tex]\( |x + 4| = -6 \)[/tex], we need to understand the properties of absolute value functions. The absolute value of a number is always non-negative, meaning it can never be less than zero. It represents the distance of a number from zero on the number line, which is always a positive value or zero.

Given the equation [tex]\( |x + 4| = -6 \)[/tex]:

1. Absolute Value Properties: The absolute value, denoted by the vertical bars [tex]\( |\cdot| \)[/tex], is defined as:
- [tex]\( |a| = a \)[/tex] if [tex]\( a \geq 0 \)[/tex]
- [tex]\( |a| = -a \)[/tex] if [tex]\( a < 0 \)[/tex]

2. Assessment of the Given Equation: Here, the right side of the equation is [tex]\(-6\)[/tex]. Absolute value expressions can never be negative. Hence, an equation where [tex]\( |x + 4| \)[/tex] is set equal to a negative number has no valid solutions.

Since the left side of the equation involves the absolute value of [tex]\( x + 4 \)[/tex], and the absolute value cannot be equal to a negative number, there are no real numbers [tex]\( x \)[/tex] that satisfy this equation.

Thus, the solution to the equation [tex]\( |x + 4| = -6 \)[/tex] is:

A. No solution.

So, the answer is:

A. No solution.