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.
