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

A. \{10\}
B. \{-10\}
C. \{-10, 10\}
D. no solution

Sagot :

GinnyAnswer
To solve the equation [tex]\( |-x| = -10 \)[/tex], let's analyze the components of the equation step-by-step:

1. Understanding Absolute Value:
- The absolute value of a number [tex]\( |a| \)[/tex] is defined as the non-negative value of [tex]\( a \)[/tex]. This means [tex]\( |a| \geq 0 \)[/tex] for any real number [tex]\( a \)[/tex].

2. Setting Up the Equation:
- The equation [tex]\( |-x| = -10 \)[/tex] states that the absolute value of [tex]\(-x\)[/tex] is equal to [tex]\(-10\)[/tex].

3. Properties of Absolute Value:
- By definition, the absolute value [tex]\( |y| \)[/tex] of any number [tex]\( y \)[/tex] is always non-negative: [tex]\( |y| \geq 0 \)[/tex].

4. Analyzing the Given Equation:
- In our case, the equation [tex]\( |-x| = -10 \)[/tex] tells us that a non-negative number [tex]\( |-x| \)[/tex] is equal to a negative number [tex]\(-10\)[/tex].

5. Conclusion:
- Since the absolute value [tex]\( |-x| \)[/tex] cannot be negative (as [tex]\( |y| \geq 0 \)[/tex]), it is impossible for [tex]\( |-x| \)[/tex] to equal [tex]\(-10\)[/tex].

Therefore, there is no real number [tex]\( x \)[/tex] that satisfies the equation [tex]\( |-x| = -10 \)[/tex]. Thus, the solution set is:

no solution.
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