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What is the solution set of [tex]$|-x|=-10?$[/tex]

A. \{10\}
B. [tex]$\{-10\}$[/tex]
C. [tex]$\{-10, 10\}$[/tex]
D. no solution


Sagot :

Let's analyze the equation [tex]\( |-x| = -10 \)[/tex] step by step.

The absolute value function, [tex]\( |x| \)[/tex], always results in a non-negative value. This means that for any real number [tex]\( x \)[/tex], the result of [tex]\( |x| \)[/tex] is always greater than or equal to zero.

Given the expression [tex]\( |-x| \)[/tex]:
- We know that [tex]\( |-x| = |x| \)[/tex] because the absolute value of [tex]\(-x\)[/tex] is the same as the absolute value of [tex]\( x \)[/tex].

So, the equation [tex]\( |-x| = -10 \)[/tex] can be rewritten as:
[tex]\[ |x| = -10 \][/tex]

However, [tex]\( |x| \)[/tex] can never be negative. The absolute value is defined such that it always yields a non-negative result. Therefore, there is no value of [tex]\( x \)[/tex] that satisfies this equation.

Based on this logical reasoning, we conclude that the equation [tex]\( |-x| = -10 \)[/tex] has no solution.

Thus, the solution set is:

[tex]\[ \text{no solution} \][/tex]