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]
