To determine which of the given options are solutions to the equation [tex]\(1x = 0\)[/tex], we need to evaluate each option separately and see if they satisfy the equation.
The given equation [tex]\(1x = 0\)[/tex] simplifies to [tex]\(x = 0\)[/tex].
Let's assess each option:
Option A: 0
- Substituting [tex]\(x = 0\)[/tex] into the equation [tex]\(1x = 0\)[/tex]:
[tex]\[
1 \times 0 = 0
\][/tex]
This is true since [tex]\(0 = 0\)[/tex]. Therefore, 0 is indeed a solution.
Option B: All positive numbers
- Consider any positive number, for example, [tex]\(x = 1\)[/tex]:
[tex]\[
1 \times 1 = 1
\][/tex]
This is false because [tex]\(1 \neq 0\)[/tex]. Therefore, not all positive numbers can be solutions.
Option C: All negative numbers
- Consider any negative number, for example, [tex]\(x = -1\)[/tex]:
[tex]\[
1 \times -1 = -1
\][/tex]
This is false because [tex]\(-1 \neq 0\)[/tex]. Therefore, no negative numbers can be solutions.
Option D: None of these
- This option is incorrect because we identified that 0 is indeed a solution from Option A.
Based on this evaluation, the solutions to the equation [tex]\(1x = 0\)[/tex] are:
A. 0 ☐
B. All positive numbers
C. All negative numbers
D. None of these
