Let's analyze the given equation:
[tex]\[
-13 = -4
\][/tex]
Firstly, observe that there's no variable [tex]\( x \)[/tex] or any other variable included in this equation. We simply have the constants -13 and -4.
Now, let's consider the basic properties of equality. For two numbers to be equal, they must have the same value. However, in this case, -13 and -4 are clearly not the same value. Specifically, -13 is less than -4. This makes the equation:
[tex]\[
-13 = -4
\][/tex]
false under any mathematical norms or number properties.
Given the options provided:
A. [tex]\( x = 9 \)[/tex]
B. [tex]\( x = 17 \)[/tex]
C. [tex]\( x = -9 \)[/tex]
D. [tex]\( x = -17 \)[/tex]
None of these options will make the equation valid since the equation itself, [tex]\( -13 = -4 \)[/tex], is inherently inconsistent and cannot be true under any circumstances. Therefore, there is no value of [tex]\( x \)[/tex] that can satisfy this equation, indicating that none of the options (A, B, C, or D) are correct.
Hence, the correct response is that the equation has no solution. None of the given options are correct.
