Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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

A. [tex]\{10\}[/tex]

B. [tex]\{-10\}[/tex]

C. [tex]\{-10, 10\}[/tex]

D. No solution

Sagot :

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

1. Understanding the Absolute Value Function: The absolute value function, denoted as [tex]\(|a|\)[/tex], always outputs non-negative results. In mathematical terms, [tex]\(|a| \geq 0\)[/tex] for any real number [tex]\(a\)[/tex].

2. Applying Absolute Value to [tex]\(-x\)[/tex]: In our equation, the expression is [tex]\(|-x|\)[/tex]. Since the absolute value of any number is always non-negative, we have that [tex]\(|-x| \geq 0\)[/tex]. This means that for any value of [tex]\(x\)[/tex], [tex]\( |-x| \)[/tex] will always be a non-negative number (greater than or equal to 0).

3. Comparing with [tex]\(-10\)[/tex]: The equation states [tex]\( |-x| = -10 \)[/tex]. Here, [tex]\(-10\)[/tex] is a negative number. Since the left side of the equation (which is [tex]\(|-x|\)[/tex]) is always non-negative, it can never be equal to a negative number like [tex]\(-10\)[/tex].

4. Conclusion: Therefore, the equation [tex]\( |-x| = -10 \)[/tex] has no possible solutions. The non-negativity property of absolute values ensures that no value of [tex]\(x\)[/tex] will satisfy this equation.

Thus, the solution set of [tex]\( |-x| = -10 \)[/tex] is:
[tex]\[ \text{no solution} \][/tex]